Recent theoretical progress indicates that spacetime and gravity emerge together from the entangl... more Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional ‘dark’ gravitational force describing the ‘elastic’ response due to the entrop...
A low vs. high glycemic index of a high-fat (HF) diet (LGI and HGI, respectively) significantly r... more A low vs. high glycemic index of a high-fat (HF) diet (LGI and HGI, respectively) significantly retarded adverse health effects in adult male C57BL/6J mice, as shown recently (Van Schothorst EM, Bunschoten A, Schrauwen P, Mensink RP, Keijer J. FASEB J 23: 1092–1101, 2009). The LGI diet enhanced whole body insulin sensitivity and repressed HF diet-induced body and white adipose tissue (WAT) weight gain, resulting in significantly reduced serum leptin and resistin levels and increased adiponectin levels. We questioned how WAT is modulated and characterized the molecular mechanisms underlying the glycemic index-mediated effects using whole genome microarrays. This showed that the LGI diet mainly exerts its beneficial effects via substrate metabolism, especially fatty acid metabolism. In addition, cell adhesion and cytoskeleton remodeling showed reduced expression, in line with lower WAT mass. An important transcription factor showing enhanced expression is PPAR-γ. Furthermore, serum le...
We investigate the possibility that the geometry dual to a typical AdS black hole microstate corr... more We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model an...
In these notes we give a review of topological string theory. We discuss twodimensional topologic... more In these notes we give a review of topological string theory. We discuss twodimensional topological field theories, which represent its classical backgrounds. We describe their symmetries and the properties of the physical amplitudes. In the particular context of d < 1 we explain how topological string theory can be exactly solved, by deriving Schwinger-Dyson equations in the form of recursion relations between world-sheet correlation functions at different genera. ∗Based on lectures presented at the Spring School on Strings and Quantum Gravity, Trieste, April 24 – May 2, 1990 and the Cargése Workshop on Random Surfaces, Quantum Gravity and Strings, May 28 – June 1, 1990.
We study the low energy effective action S of gravity, induced by integrating out gauge and matte... more We study the low energy effective action S of gravity, induced by integrating out gauge and matter fields, in a general class of RS-type string compactification scenarios with exponential warp factors. Our method combines dimensional reduction with the holographic map between between 5-d supergravity and 4-d large N field theory. Using the classical supergravity approximation, we derive a flow equation of the effective action S that controls its behavior under scale transformations. We find that as a result each extremum of S automatically describes a complete RG trajectory of classical solutions. This implies that, provided the cosmological constant is canceled in the high energy theory, classical flat space backgrounds naturally remain stable under the RG-flow. The mechanism responsible for this stability is that the non-zero vacuum energy generated by possible phase transitions, is absorbed by a dynamical adjustment of the contraction rate of the warp factor.
We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from thre... more We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies an auxiliary system acting as a heat bath both at I+ and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at I+ naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page time, and neither observer wi...
The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in... more The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N = 4, d = 4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the root system as the extended S-duality group PGL(2,Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant two-centered solutions. This leads to an interpretation for the Weyl group as the group of wall-crossing, or the group of discrete attractor flows. Furthermore we propose an equivalence between a "second-quantized multiplicity" of a charge- and moduli- dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wall-crossing formula obtained from the supergravity analysis. This can be thought of as providing a microscopic derivation of the wall-cr...
Motivated by the vast success of deep convolutional networks, there is a great interest in genera... more Motivated by the vast success of deep convolutional networks, there is a great interest in generalizing convolutions to non-Euclidean manifolds. A major complication in comparison to flat spaces is that it is unclear in which alignment a convolution kernel should be applied on a manifold. The underlying reason for this ambiguity is that general manifolds do not come with a canonical choice of reference frames (gauge). Kernels and features therefore have to be expressed relative to arbitrary coordinates. We argue that the particular choice of coordinatization should not affect a network's inference -- it should be coordinate independent. A simultaneous demand for coordinate independence and weight sharing is shown to result in a requirement on the network to be equivariant under local gauge transformations (changes of local reference frames). The ambiguity of reference frames depends thereby on the G-structure of the manifold, such that the necessary level of gauge equivariance i...
We investigate the possibility that the geometry dual to a typical AdS black hole microstate corr... more We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturbations of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.
The microscopic description of AdS space obeys the holographic principle in the sense that the nu... more The microscopic description of AdS space obeys the holographic principle in the sense that the number of microscopic degrees of freedom is given by the area of the holographic boundary. We assume the same applies to the microscopic holographic theories for non-AdS spacetimes, specifically for Minkowski, de Sitter, and AdS below its curvature radius. By taking general lessons from AdS/CFT we derive the cutoff energy of the holographic theories for these non-AdS geometries. Contrary to AdS/CFT, the excitation energy decreases towards the IR in the bulk, which is related to the negative specific heat of black holes. We construct a conformal mapping between the non-AdS geometries and AdS 3 × S q spacetimes, and relate the microscopic properties of the holographic theories for non-AdS spaces to those of symmetric product CFTs. We find that the mechanism responsible for the inversion of the energy-distance relation corresponds to the long string phenomenon. This same mechanism naturally explains the negative specific heat for non-AdS black holes and the value of the vacuum energy in (A)dS spacetimes.
We argue that the region behind the horizon of a one-sided black hole can be probed by an analogu... more We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form $$ \mathcal{O}\tilde{\mathcal{O}} $$ O O ˜ , where $$ \tilde{\mathcal{O}} $$ O ˜ denote the state-dependent “mirror operators”. We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.
The topological correlation functions, their prepotential, and the Landau-Ginzburg potential are ... more The topological correlation functions, their prepotential, and the Landau-Ginzburg potential are computed for the N= 2 supersymmetric, c= 3, matter model that is a tensor product of'three c= 1 models. An interesting class of N= 2 superconformal field theories are the ones that allow a Landau-Ginzburg description [ 1 ] in terms ofa superpotential W(XA). This function Wencodes important geometrical information about the target space of the SCFT, for example, for c=9 SCFT corresponding to Calabi-Yau space the algebraic equation W(xA) =0 (1) describes the C-Y manifold embedded in a (weighted) projective space. An important role in these theories is played by the chiral primary fields. They describe the inequivalent variations of the potential W and in particular there is a canonical identification between the marginal chiral, primary fields ~i, and (possibly a subset of) the infinitesimal variations of the moduli t,. In superstring compactifications the structure constants C,)~. of the chiral primary ring give the Yukawa couplings of the massless scalar fields corresponding to the moduli ti. In this context it is known that due to the "special geometry" of the C-Y moduli space [ 2 ] these Yukawa couplings can be expressed in terms of a single "prepotential" .~-(t~) as 03.~ C,jk= 0ti Otj Otk " (2) This equation played an important role in the recent beautiful work of Candelas et al. [ 3 ], who computed z~ for the case of the mirror manifold of the quintic hypersurface. Recently in a different development this same relation (2) was discovered in the context of perturbed topological CFT [ 4 ], obtained by "twisting" N= 2 SCFT [ 5 ]. In this case the relation (2) is derived by applying the two-dimensional Ward identities to the perturbed three-point functions where ~} j-I) _ G-~/2 G_-~/2~z. In fact, (2) does not only hold for the marginal deformations, but also when we take ti to be the coupling constants of the other chiral primary fields. The prepotential .~-has the interpretation
As was shown by Aharony, Hanany and Kol and independently by Sen, type IIB string theory admits c... more As was shown by Aharony, Hanany and Kol and independently by Sen, type IIB string theory admits configurations where strings of different charges (p i , q i) form so-called string networks. We argue that these networks blow up into "supersheets": supersymmetric spinning cylindrical D3-branes carrying electric and magnetic fluxes. These supersheets are three-dimensional generalizations of the supertubes that were constructed by Mateos and Townsend. We calculate the mass of both systems for arbitrary values of the parameters and find exact agreement.
We extend the recent proposal of Papadodimas and Raju of a CFT construction of operators inside t... more We extend the recent proposal of Papadodimas and Raju of a CFT construction of operators inside the black hole interior to arbitrary non-maximally mixed states. Our construction builds on the general prescription given in earlier work, based on ideas from quantum error correction. We indicate how the CFT state dependence of the interior modes can be removed by introducing an external system, such as an observer, that is entangled with the CFT.
Previous studies of high-energy scattering in QCD have shown a remarkable correspondence with two... more Previous studies of high-energy scattering in QCD have shown a remarkable correspondence with two-dimensional field theory. In this paper we formulate a simple effective model in which this two-dimensional nature of the interactions is manifest. Starting from the (3+1)-dimensional Yang-Mills action, we implement the high energy limit s >> t via a scaling argument and we derive from this a simplified effective theory. This effective theory is still (3+1)-dimensional, but we show that its interactions can to leading order be summarized in terms of a two-dimensional sigma-model defined on the transverse plane. Finally, we verify that our formulation is consistent with known perturbative results. * For the case the particles have only electromagnetic interactions, this shockwave interaction has been used in [4, 5] to give an elegant derivation of the high energy scattering amplitude, reproducing the result obtained via the eikonal approximation [6, 7]. Related work in gravity has been done in [4, 8, 9].
We investigate Penrose limits of two classes of non-local theories, little string theories and no... more We investigate Penrose limits of two classes of non-local theories, little string theories and non-commutative gauge theories. Penrose limits of the near-horizon geometry of NS5-branes help to shed some light on the high energy spectrum of little string theories. We attempt to understand renormalization group flow in these theories by considering Penrose limits wherein the null geodesic also has a radial component. In particular, we demonstrate that it is possible to construct a pp-wave spacetime which interpolates between the linear dilaton and the AdS regions for the Type IIA NS5-brane. Similar analysis is considered for the holographic dual geometry to non-commutative field theories. May 2002.
Recent theoretical progress indicates that spacetime and gravity emerge together from the entangl... more Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional ‘dark’ gravitational force describing the ‘elastic’ response due to the entrop...
A low vs. high glycemic index of a high-fat (HF) diet (LGI and HGI, respectively) significantly r... more A low vs. high glycemic index of a high-fat (HF) diet (LGI and HGI, respectively) significantly retarded adverse health effects in adult male C57BL/6J mice, as shown recently (Van Schothorst EM, Bunschoten A, Schrauwen P, Mensink RP, Keijer J. FASEB J 23: 1092–1101, 2009). The LGI diet enhanced whole body insulin sensitivity and repressed HF diet-induced body and white adipose tissue (WAT) weight gain, resulting in significantly reduced serum leptin and resistin levels and increased adiponectin levels. We questioned how WAT is modulated and characterized the molecular mechanisms underlying the glycemic index-mediated effects using whole genome microarrays. This showed that the LGI diet mainly exerts its beneficial effects via substrate metabolism, especially fatty acid metabolism. In addition, cell adhesion and cytoskeleton remodeling showed reduced expression, in line with lower WAT mass. An important transcription factor showing enhanced expression is PPAR-γ. Furthermore, serum le...
We investigate the possibility that the geometry dual to a typical AdS black hole microstate corr... more We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model an...
In these notes we give a review of topological string theory. We discuss twodimensional topologic... more In these notes we give a review of topological string theory. We discuss twodimensional topological field theories, which represent its classical backgrounds. We describe their symmetries and the properties of the physical amplitudes. In the particular context of d < 1 we explain how topological string theory can be exactly solved, by deriving Schwinger-Dyson equations in the form of recursion relations between world-sheet correlation functions at different genera. ∗Based on lectures presented at the Spring School on Strings and Quantum Gravity, Trieste, April 24 – May 2, 1990 and the Cargése Workshop on Random Surfaces, Quantum Gravity and Strings, May 28 – June 1, 1990.
We study the low energy effective action S of gravity, induced by integrating out gauge and matte... more We study the low energy effective action S of gravity, induced by integrating out gauge and matter fields, in a general class of RS-type string compactification scenarios with exponential warp factors. Our method combines dimensional reduction with the holographic map between between 5-d supergravity and 4-d large N field theory. Using the classical supergravity approximation, we derive a flow equation of the effective action S that controls its behavior under scale transformations. We find that as a result each extremum of S automatically describes a complete RG trajectory of classical solutions. This implies that, provided the cosmological constant is canceled in the high energy theory, classical flat space backgrounds naturally remain stable under the RG-flow. The mechanism responsible for this stability is that the non-zero vacuum energy generated by possible phase transitions, is absorbed by a dynamical adjustment of the contraction rate of the warp factor.
We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from thre... more We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies an auxiliary system acting as a heat bath both at I+ and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at I+ naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page time, and neither observer wi...
The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in... more The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N = 4, d = 4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the root system as the extended S-duality group PGL(2,Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant two-centered solutions. This leads to an interpretation for the Weyl group as the group of wall-crossing, or the group of discrete attractor flows. Furthermore we propose an equivalence between a "second-quantized multiplicity" of a charge- and moduli- dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wall-crossing formula obtained from the supergravity analysis. This can be thought of as providing a microscopic derivation of the wall-cr...
Motivated by the vast success of deep convolutional networks, there is a great interest in genera... more Motivated by the vast success of deep convolutional networks, there is a great interest in generalizing convolutions to non-Euclidean manifolds. A major complication in comparison to flat spaces is that it is unclear in which alignment a convolution kernel should be applied on a manifold. The underlying reason for this ambiguity is that general manifolds do not come with a canonical choice of reference frames (gauge). Kernels and features therefore have to be expressed relative to arbitrary coordinates. We argue that the particular choice of coordinatization should not affect a network's inference -- it should be coordinate independent. A simultaneous demand for coordinate independence and weight sharing is shown to result in a requirement on the network to be equivariant under local gauge transformations (changes of local reference frames). The ambiguity of reference frames depends thereby on the G-structure of the manifold, such that the necessary level of gauge equivariance i...
We investigate the possibility that the geometry dual to a typical AdS black hole microstate corr... more We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturbations of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.
The microscopic description of AdS space obeys the holographic principle in the sense that the nu... more The microscopic description of AdS space obeys the holographic principle in the sense that the number of microscopic degrees of freedom is given by the area of the holographic boundary. We assume the same applies to the microscopic holographic theories for non-AdS spacetimes, specifically for Minkowski, de Sitter, and AdS below its curvature radius. By taking general lessons from AdS/CFT we derive the cutoff energy of the holographic theories for these non-AdS geometries. Contrary to AdS/CFT, the excitation energy decreases towards the IR in the bulk, which is related to the negative specific heat of black holes. We construct a conformal mapping between the non-AdS geometries and AdS 3 × S q spacetimes, and relate the microscopic properties of the holographic theories for non-AdS spaces to those of symmetric product CFTs. We find that the mechanism responsible for the inversion of the energy-distance relation corresponds to the long string phenomenon. This same mechanism naturally explains the negative specific heat for non-AdS black holes and the value of the vacuum energy in (A)dS spacetimes.
We argue that the region behind the horizon of a one-sided black hole can be probed by an analogu... more We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form $$ \mathcal{O}\tilde{\mathcal{O}} $$ O O ˜ , where $$ \tilde{\mathcal{O}} $$ O ˜ denote the state-dependent “mirror operators”. We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.
The topological correlation functions, their prepotential, and the Landau-Ginzburg potential are ... more The topological correlation functions, their prepotential, and the Landau-Ginzburg potential are computed for the N= 2 supersymmetric, c= 3, matter model that is a tensor product of'three c= 1 models. An interesting class of N= 2 superconformal field theories are the ones that allow a Landau-Ginzburg description [ 1 ] in terms ofa superpotential W(XA). This function Wencodes important geometrical information about the target space of the SCFT, for example, for c=9 SCFT corresponding to Calabi-Yau space the algebraic equation W(xA) =0 (1) describes the C-Y manifold embedded in a (weighted) projective space. An important role in these theories is played by the chiral primary fields. They describe the inequivalent variations of the potential W and in particular there is a canonical identification between the marginal chiral, primary fields ~i, and (possibly a subset of) the infinitesimal variations of the moduli t,. In superstring compactifications the structure constants C,)~. of the chiral primary ring give the Yukawa couplings of the massless scalar fields corresponding to the moduli ti. In this context it is known that due to the "special geometry" of the C-Y moduli space [ 2 ] these Yukawa couplings can be expressed in terms of a single "prepotential" .~-(t~) as 03.~ C,jk= 0ti Otj Otk " (2) This equation played an important role in the recent beautiful work of Candelas et al. [ 3 ], who computed z~ for the case of the mirror manifold of the quintic hypersurface. Recently in a different development this same relation (2) was discovered in the context of perturbed topological CFT [ 4 ], obtained by "twisting" N= 2 SCFT [ 5 ]. In this case the relation (2) is derived by applying the two-dimensional Ward identities to the perturbed three-point functions where ~} j-I) _ G-~/2 G_-~/2~z. In fact, (2) does not only hold for the marginal deformations, but also when we take ti to be the coupling constants of the other chiral primary fields. The prepotential .~-has the interpretation
As was shown by Aharony, Hanany and Kol and independently by Sen, type IIB string theory admits c... more As was shown by Aharony, Hanany and Kol and independently by Sen, type IIB string theory admits configurations where strings of different charges (p i , q i) form so-called string networks. We argue that these networks blow up into "supersheets": supersymmetric spinning cylindrical D3-branes carrying electric and magnetic fluxes. These supersheets are three-dimensional generalizations of the supertubes that were constructed by Mateos and Townsend. We calculate the mass of both systems for arbitrary values of the parameters and find exact agreement.
We extend the recent proposal of Papadodimas and Raju of a CFT construction of operators inside t... more We extend the recent proposal of Papadodimas and Raju of a CFT construction of operators inside the black hole interior to arbitrary non-maximally mixed states. Our construction builds on the general prescription given in earlier work, based on ideas from quantum error correction. We indicate how the CFT state dependence of the interior modes can be removed by introducing an external system, such as an observer, that is entangled with the CFT.
Previous studies of high-energy scattering in QCD have shown a remarkable correspondence with two... more Previous studies of high-energy scattering in QCD have shown a remarkable correspondence with two-dimensional field theory. In this paper we formulate a simple effective model in which this two-dimensional nature of the interactions is manifest. Starting from the (3+1)-dimensional Yang-Mills action, we implement the high energy limit s >> t via a scaling argument and we derive from this a simplified effective theory. This effective theory is still (3+1)-dimensional, but we show that its interactions can to leading order be summarized in terms of a two-dimensional sigma-model defined on the transverse plane. Finally, we verify that our formulation is consistent with known perturbative results. * For the case the particles have only electromagnetic interactions, this shockwave interaction has been used in [4, 5] to give an elegant derivation of the high energy scattering amplitude, reproducing the result obtained via the eikonal approximation [6, 7]. Related work in gravity has been done in [4, 8, 9].
We investigate Penrose limits of two classes of non-local theories, little string theories and no... more We investigate Penrose limits of two classes of non-local theories, little string theories and non-commutative gauge theories. Penrose limits of the near-horizon geometry of NS5-branes help to shed some light on the high energy spectrum of little string theories. We attempt to understand renormalization group flow in these theories by considering Penrose limits wherein the null geodesic also has a radial component. In particular, we demonstrate that it is possible to construct a pp-wave spacetime which interpolates between the linear dilaton and the AdS regions for the Type IIA NS5-brane. Similar analysis is considered for the holographic dual geometry to non-commutative field theories. May 2002.
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Papers by Erik Verlinde