Papers by Anatoly Dymarsky
Physical Review Letters
We show that presence of transport imposes constraints on matrix elements entering the Eigenstate... more We show that presence of transport imposes constraints on matrix elements entering the Eigenstate Thermalization Hypothesis (ETH) ansatz and require them to be correlated. It is generally assumed that the ETH ansatz reduces to Random Matrix Theory (RMT) below the Thouless energy scale. We show this conventional picture is not self-consistent. We prove that the energy scale at which ETH ansatz reduces to RMT has to be parametrically smaller than the inverse timescale of the slowest thermalization mode present in the system. In particular it has to be parametrically smaller than the Thouless energy. Our results indicate there is a new scale relevant for thermalization dynamics.
Physical Review Letters, 2022
We show there exist UV-complete field-theoretic models in general dimension, including 2+1, with ... more We show there exist UV-complete field-theoretic models in general dimension, including 2+1, with the spontaneous breaking of a global symmetry, which persists to the arbitrarily high temperatures. Our example is a conformal vector model with the O(N) × Z2 symmetry at zero temperature. Using conformal perturbation theory we establish Z2 symmetry is broken at finite temperature for N > 17. Similar to recent constructions of [1, 2], in the infinite N limit our model has a non-trivial conformal manifold, a moduli space of vacua, which gets deformed at finite temperature. Furthermore, in this regime the model admits a persistent breaking of O(N) in 2 + 1 dimensions, therefore providing another example where the Coleman-Hohenberg-Mermin-Wagner theorem can be bypassed.
ArXiv, 2022
Modern power systems face a grand challenge in grid management due to increased electricity deman... more Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can compromise grid security. The security assessment is directly connected to the robustness of the operating condition and is evaluated by analyzing proximity to the power flow solution space’s boundary. Calculating location of such a boundary is a computationally challenging task, linked to the power flow equations’ non-linear nature, presence of technological constraints, and complicated network topology. In this paper we introduce a general framework to characterize points on the power flow solution space boundary in terms of auxiliary variables subject to algebraic constraints. Then we develop an adaptive continuation algorithm to trace 1-dimensional sections of boundary curves which exhibits robust performance and computational tractability. Implementation of the algorithm is described in detai...
Journal of High Energy Physics, 2021
We construct a map between a class of codes over F4 and a family of non-rational Narain CFTs. Thi... more We construct a map between a class of codes over F4 and a family of non-rational Narain CFTs. This construction is complementary to a recently introduced relation between quantum stabilizer codes and a class of rational Narain theories. From the modular bootstrap point of view we formulate a polynomial ansatz for the partition function which reduces modular invariance to a handful of algebraic easy-to-solve constraints. For certain small values of central charge our construction yields optimal theories, i.e. those with the largest value of the spectral gap.
Journal of High Energy Physics, 2020
We construct black hole geometries in AdS 3 with non-trivial values of KdV charges. The black hol... more We construct black hole geometries in AdS 3 with non-trivial values of KdV charges. The black holes are holographically dual to quantum KdV Generalized Gibbs Ensemble in 2d CFT. They satisfy thermodynamic identity and thus are saddle point configurations of the Euclidean gravity path integral. We discuss holographic calculation of the KdV generalized partition function and show that for a certain value of chemical potentials new geometries, not the conventional BTZ ones, are the leading saddles.
Physical Review Letters, 2019
Journal of Statistical Mechanics: Theory and Experiment, 2018
We investigate the eigenstate thermalization hypothesis (ETH) in d+1 dimensional conformal field ... more We investigate the eigenstate thermalization hypothesis (ETH) in d+1 dimensional conformal field theories by studying reduced density matrices in energy eigenstates. We show that if local probes of high energy primary eigenstates satisfy ETH, then any finite energy observable with support on a subsystem of finite size satisfies ETH. In two dimensions, we discover that if ETH holds locally, the finite size reduced density matrix of states created by heavy primary operators is well-approximated by a projection to the Virasoro identity block.
Journal of High Energy Physics, 2016
This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field... more This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unless the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.
Linear Algebra and its Applications, 2016
We derive an upper bound on the size of a ball such that the image of the ball under quadratic ma... more We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak [1] in the case of quadratic map. We also generalize the notion of the joint numerical range of m-tuple of matrices by adding vector-dependent inhomogeneous terms and provide a sufficient condition for its convexity.
Journal of High Energy Physics, 2015
We study the implications of scale invariance in four-dimensional quantum field theories. Imposin... more We study the implications of scale invariance in four-dimensional quantum field theories. Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration. This vanishing is a nontrivial necessary condition for conformality. We provide an argument why this is expected to be a sufficient condition as well, thereby linking scale and conformal invariance in unitary theories. We also discuss possible exceptions to our argument.
Journal of High Energy Physics, 2012
We find a new family of non-supersymmetric numerical solutions of IIB supergravity which are dual... more We find a new family of non-supersymmetric numerical solutions of IIB supergravity which are dual to the $ \mathcal{N} = 1 $ cascading “conifold” theory perturbed by certain combinations of relevant single trace and marginal double trace operators with non infinitesimal couplings. The SUSY is broken but the resulting ground states, and their gravity duals, remain stable, at least perturbatively. Despite the complicated field theory dynamics the gravity solutions have a simple structure. They feature the Ricci-flat non-Kähler metric on the deformed conifold and the imaginary self-dual three-form flux accompanied by a constant dilaton.
Progress in String, Field and Particle Theory, 2003
S-CHARGE MONODROMY MECHANISM IN N= 2 SYM FROM SEMICLASSICAL POINT OF VIEW ANATOLY DYMARSKY AND DM... more S-CHARGE MONODROMY MECHANISM IN N= 2 SYM FROM SEMICLASSICAL POINT OF VIEW ANATOLY DYMARSKY AND DMITRY MELNIKOV ITEP, B. Cheremushkinskaja, 25, Moscow, Russia Abstract. We consider a monopole in N= 2 SYM near the point, where ...
The logarithmic running of marginal double-trace operators is a general feature of 4-d field theo... more The logarithmic running of marginal double-trace operators is a general feature of 4-d field theories containing scalar fields in the adjoint or bifundamental representation. Such operators provide leading contributions in the large N limit; therefore, the leading terms in their beta functions must vanish for a theory to be large N conformal. We calculate the one-loop beta functions in orbifolds of the N = 4 SYM theory by a discrete subgroup Γ of the SU(4) R-symmetry, which are dual to string theory on AdS 5 × S 5 /Γ. We present a general strategy for determining whether there is a fixed line passing through the origin of the coupling constant space. Then we study in detail some classes of non-supersymmetric orbifold theories, and emphasize the importance of decoupling the U(1) factors. Among our examples, which include orbifolds acting freely on the S 5 , we do not find any large N non-supersymmetric theories with fixed lines passing through the origin. Connection of these results with closed string tachyon condensation in AdS 5 × S 5 /Γ is discussed.
We carry out a thorough analysis of the moduli space of the cascading gauge theory found on p D3-... more We carry out a thorough analysis of the moduli space of the cascading gauge theory found on p D3-branes and M wrapped D5-branes at the tip of the conifold. We find various mesonic branches of the moduli space whose string duals involve the warped deformed conifold with different numbers of mobile D3-branes. The branes that are not mobile form a BPS bound state at threshold. In the special case where p is divisible by M there also exists a one-dimensional baryonic branch whose family of supergravity duals, the resolved warped deformed conifolds, was constructed recently. The warped deformed conifold is a special case of these backgrounds where the resolution parameter vanishes and a Z 2 symmetry is restored. We study various brane probes on the resolved warped deformed conifolds, and successfully match the results with the gauge theory. In particular, we show that the radial potential for a D3-brane on this space varies slowly, suggesting a new model of D-brane inflation.
The Klebanov-Strassler background is invariant under the Z 2 symmetry I, which acts by exchanging... more The Klebanov-Strassler background is invariant under the Z 2 symmetry I, which acts by exchanging the bi-fundamental fields A and B, accompanied by the charge conjugation. We study the background perturbations in the I-odd sector and find an exhaustive list of bosonic states invariant under the global SU(2)×SU(2) symmetry. In addition to the scalars identified in an earlier publication arXiv: 0712.4404 we find 7 families of massive states of spin 1. Together with the spin 0 states they form 3 families of massive vector multiplets and 2 families of massive gravitino multiplets, containing a vector, a pseudovector and fermions of spin 3/2 and 1/2. In the conformal Klebanov-Witten case these I-odd particles belong to the N = 1 superconformal Vector Multiplet I and Gravitino Multiplets II and IV. The operators dual to the I-odd singlet sector include those without bi-fundamental fields making an interesting connection with the pure N = 1 SYM theory. We calculate the mass spectrum of the corresponding glueballs numerically and discuss possible applications of our results.
We study probe flavor branes supersymmetrically embedded in the Klebanov-Strassler background. Th... more We study probe flavor branes supersymmetrically embedded in the Klebanov-Strassler background. The embedding is controlled by a single complex parameter µ related to the quark mass. We study the spectrum of the vector mesons as a function of µ and compare it with the experimental data. Assuming that the ρ(2150) meson is a 3 3 S 1 mode we find a remarkable agreement with the masses of the lightest excited ρ-mesons. Also, for a certain range of parameters our model exhibits an unusual behavior. The mesons built of the lighter quarks become more heavy than the ones built of the heavier quarks. We comment on a possible connection this phenomenon may have with the masses of the putative pure strange-anti strange mesons.
We study supersymmetric vacua of the N = 1 cascading SU(M + p) × SU(p) gauge theory with flavor-t... more We study supersymmetric vacua of the N = 1 cascading SU(M + p) × SU(p) gauge theory with flavor-the theory on p D3-branes and M wrapped D5-branes at the tip of the conifold, and N f flavor D7-branes wrapping a holomorphic four-cycle inside the conifold. The Coulomb branch of the moduli space is inherited from the pure gauge theory without flavor and was thoroughly studied in the past. Besides, there is a Higgs branch where some D3 and/or D5-branes dissolve in the D7-branes forming the worldvolume gauge instantons. We study the Higgs branch both from the field theory and the bulk point of view. On the classical level the moduli space is closely related to the one of the N = 2 C 2 /Z 2 orbifold theory, in particular certain vacua of the N = 1 theory are related to noncommutative instantons on the resolved C 2 /Z 2. On the quantum level the Higgs branch acquires corrections due to renormalization of the Kähler potential and non-perturbative effects in field theory. In the bulk this is encoded in the classical D7-brane geometry. We compute the VEVs of the protected operators and the field theory RG flow and find an agreement with the parallel computations in the bulk.
Journal of High Energy Physics, 2007
We provide new evidence for the gauge/string duality between the baryonic branch of the cascading... more We provide new evidence for the gauge/string duality between the baryonic branch of the cascading SU (k(M + 1)) × SU (kM) gauge theory and a family of type IIB flux backgrounds based on warped products of the deformed conifold and R 3,1. We show that a Euclidean D5-brane wrapping all six deformed conifold directions can be used to measure the baryon expectation values, and present arguments based on κ-symmetry and the equations of motion that identify the gauge bundles required to ensure worldvolume supersymmetry of this object. Furthermore, we investigate its coupling to the pseudoscalar and scalar modes associated with the phase and magnitude, respectively, of the baryon expectation value. We find that these massless modes perturb the Dirac-Born-Infeld and Chern-Simons terms of the D5-brane action in a way consistent with our identification of the baryonic condensates. We match the scaling dimension of the baryon operators computed from the D5-brane action with that found in the cascading gauge theory. We also derive and numerically evaluate an expression that describes the variation of the baryon expectation values along the supergravity dual of the baryonic branch.
Journal of High Energy Physics, 2006
We study the potential governing D3-brane motion in a warped throat region of a string compactifi... more We study the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes. If the Kähler moduli of the compact space are stabilized by nonperturbative effects, a D3-brane experiences a force due to its interaction with D-branes wrapping certain four-cycles. We compute this interaction, as a correction to the warped four-cycle volume, using explicit throat backgrounds in supergravity. This amounts to a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume. We demonstrate for warped conical spaces that the superpotential correction is given by the embedding equation specifying the wrapped four-cycle, in agreement with the general form proposed by Ganor. Our approach automatically provides a solution to the problem of defining a holomorphic gauge coupling on wrapped D7-branes in a background with D3-branes. Finally, our results have applications to cosmological inflation models in which the inflaton is modeled by a D3-brane moving in a warped throat.
Journal of High Energy Physics, 2009
We provide a systematic treatment of possible corrections to the inflaton potential for Dbrane in... more We provide a systematic treatment of possible corrections to the inflaton potential for Dbrane inflation in the warped deformed conifold. We consider the D3-brane potential in the presence of the most general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. This corresponds to the potential on the Coulomb branch of the dual gauge theory, in the presence of arbitrary perturbations of the Lagrangian. The leading contributions arise from perturbations by the most relevant operators that do not destroy the throat geometry. We find a generic contribution from a non-chiral operator of dimension ∆ = 2 associated with a global symmetry current, resulting in a negative contribution to the inflaton mass-squared. If the Calabi-Yau preserves certain discrete symmetries, this is the dominant correction to the inflaton potential, and fine-tuning of the inflaton mass is possible. In the absence of such discrete symmetries, the dominant contribution comes from a chiral operator with ∆ = 3/2, corresponding to a φ 3/2 term in the inflaton potential. The resulting inflationary models are phenomenologically similar to the inflection point scenarios arising from specific D7-brane embeddings, but occur under far more general circumstances. Our strategy extends immediately to other warped geometries, given sufficient knowledge of the Kaluza-Klein spectrum.
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Papers by Anatoly Dymarsky