Scaling violations in Yang–Mills theories and strings in AdS5

Physical Review Letters, 2009

Using the thermodynamic Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y -system conjectured in Gromov et al. (Integrability for the Full Spectrum of Planar AdS/CFT. arXiv:0901.3753 [hep-th]) for the spectrum of all operators in planar N = 4 SYM theory follows from these equations. In particular, we present the integral TBA type equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analog of DHM formula for the dressing kernel in the mirror kinematics.

Physical Review D, 2018

The spectrum of IIB supergravity on AdS5 × S 5 contains a number of bound states described by long double-trace multiplets in N = 4 super Yang-Mills theory at large 't Hooft coupling. At large N these states are degenerate and to obtain their anomalous dimensions as expansions in 1 N 2 one has to solve a mixing problem. We conjecture a formula for the leading anomalous dimensions of all long double-trace operators which exhibits a large residual degeneracy whose structure we describe. Our formula can be related to conformal Casimir operators which arise in the structure of leading discontinuities of supergravity loop corrections to four-point correlators of half-BPS operators.

We study light-cone gauge quantization of IIB strings in AdS 5 × S 5 for small radius in Poincare coordinates. A picture of strings made up of noninteracting bits emerges in the zero radius limit. In this limit, each bit behaves like a superparticle moving in the AdS 5 × S 5 background, carrying appropriate representations of the super conformal group PSU(2, 2|4). The standard Hamiltonian operator which causes evolution in the light-cone time has continuous eigenvalues and provides a basis of states which is not suitable for comparing with the dual super Yang-Mills theory. However, there exist operators in the light-cone gauge which have discrete spectra and can be used to label the states. We obtain the spectrum of single bit states and construct multi-bit states in this basis. There are difficulties in the construction of string states from the multi-bit states, which we discuss. A non-zero value of the radius introduces interactions between the bits and the spectrum of multi-bit states gets modified. We compute the leading perturbative corrections at small radius for a few simple cases. Potential divergences in the perturbative corrections, arising from strings near the boundary, cancel. This encourages us to believe that our perturbative treatment could provide a framework for a rigorous and detailed testing of the AdS/CFT conjecture, once the difficulties in the construction of string states are resolved.

Physics Letters B, 2002

In a N = 1 superspace formulation of N = 4 Yang-Mills theory we obtain the anomalous dimensions of chiral operators with large R charge J → ∞ keeping g 2 N/J 2 finite, to all orders of perturbation theory in the planar limit. Our result proves the conjecture that the anomalous dimensions are indeed finite in the above limit. This amounts to an exact check of the proposed duality between a sector of N = 4 Yang-Mills theory with large R charge J and string theory in a pp-wave background.

Journal of High Energy Physics, 2014

We propose a new entry within the dictionary of the AdS/CFT duality at strong coupling: in the limit of a large spin or a large R-charge, the anomalous dimension of the gauge theory operator dual to a semiclassical rotating string is proportional to the string proper length. This conjecture is motivated by a generalization to strings of the rule for computing anomalous dimensions of massive particles and supergravity fields in the anti-de Sitter space. We show that this proportionality holds for a rotating closed string in global AdS space, representing a high spin operator made of fields in the adjoint representation. It is also valid for closed strings rotating in S 5 (representing operators with large R-charge), for closed strings with multiple AdS spin, and for giant magnons. Based on this conjecture, we calculate the anomalous dimension δ of operators made of fields in the fundamental representation, associated with high spin mesons, and which are represented by rotating open strings attached to probe D7-branes. The result is a logarithmic dependence upon the spin, δ ∼ √ λ ln S, similar to the closed string case. We show that the operator properties -anomalous dimension and spin -are obtained from measurements made by a local observer in the anti-de Sitter space. For the open string case, this ensures that these quantities are independent of the mass scale introduced by the D7-branes (the quark mass), as expected on physical grounds. In contrast, properties of the gauge theory states, like the energy, correspond to measurements by a gauge theory observer and depend upon the mass scale -once again, as expected.

Letters in Mathematical Physics, 2010

Using the thermodynamic Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in Gromov et al. (Integrability for the Full Spectrum of Planar AdS/CFT. arXiv:0901.3753 [hep-th]) for the spectrum of all operators in planar N = 4 SYM theory follows from these equations. In particular, we present the integral TBA type equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analog of DHM formula for the dressing kernel in the mirror kinematics.

Journal of High Energy …, 2003

We derive the spectrum of Kaluza-Klein descendants of string excitations on AdS 5 × S 5. String states are organized in long multiplets of the AdS supergroup SU (2, 2|4, R) with a rich pattern of shortenings at the higher spin enhancement point λ = 0. The string states holographically dual to the higher spin currents of SYM theory in the strict zero coupling limit are identified together with the corresponding Goldstone particles responsible for the Higgsing of the higher spin symmetry at λ = 0. Exploiting higher spin symmetry we propose a very simple yet effective mass formula and establish a one-to-one correspondence between the complete spectrum of ∆ 0 ≤ 4 string states and relevant/marginal single-trace deformations in N = 4 SYM theory at large N. To this end, we describe how to efficiently enumerate scaling operators in 'free' YM theory, with the inclusion of fermionic 'letters', by resorting to Polya theory. Comparison between the spectra of 1 4-BPS states is also presented. Finally, we discuss how to organize the spectrum of N = 4 SYM theory in SU (2, 2|4, R) supermultiplets by means of some kind of 'Eratostenes's sieve'.

Physics Letters B

We calculate the collinear anomalous dimensions in massless four-loop QCD and N = 4 supersymmetric Yang-Mills theory from the infrared poles of vertex form factors. We give very precise numerical approximations and a conjecture for the complete analytic results in both models we consider.

Nuclear Physics B, 1998

We discuss the spectrum of states of IIB supergravity on AdS 5 × S 5 in a manifest SU (2, 2/4) invariant setting. The boundary fields are described in terms of N = 4 superconformal Yang-Mills theory and the proposed correspondence between supergravity in AdS 5 and superconformal invariant singleton theory at the boundary is formulated in an N = 4 superfield covariant language.

Physical review, 2018

Operators dual to strings attached to giant graviton branes in AdS 5 ×S 5 can be described rather explicitly in the dual N = 4 super Yang-Mills theory. They have a bare dimension of order N so that for these operators the large N limit and the planar limit are distinct: summing only the planar diagrams will not capture the large N dynamics. Focusing on the one-loop SU (3) sector of the theory, we consider operators that are a small deformation of a 1 2 −BPS multi-giant graviton state. The diagonalization of the dilatation operator at one loop has been carried out, but explicit formulas for the operators of a good scaling dimension are only known when certain terms which were argued to be small, are neglected. In this article we include the terms which were neglected. The diagonalization is achieved by a novel mapping which replaces the problem of diagonalizing the dilatation operator with a system of bosons hopping on a lattice. The giant gravitons define the sites of this lattice and the open strings stretching between distinct giant gravitons define the hopping terms of the Hamiltonian. Using the lattice boson model, we argue that the lowest energy giant graviton states are obtained by distributing the momenta carried by the X and Y fields evenly between the giants with the condition that any particular giant carries only X or Y momenta, but not both.

Nuclear Physics B, 2005

Annales Henri Poincaré, 2013

We consider 1 2-BPS circular Wilson loops in a class of 5d superconformal field theories on S 5. The large N limit of the vacuum expectation values of Wilson loops are computed both by localization in the field theory and by evaluating the fundamental string and D4-brane actions in the dual massive IIA supergravity background. We find agreement in the leading large N limit for a rather general class of representations, including fundamental, anti-symmetric and symmetric representations. For single-node theories the match is straightforward, while for quiver theories, the Wilson loop can be in different representations for each node. We highlight the two special cases when the Wilson loop is in either in all symmetric or all anti-symmetric representations. In the anti-symmetric case, we find that the vacuum expectation value factorizes into distinct contributions from each quiver node. In the dual supergravity description, this corresponds to probe D4-branes wrapping internal S 3 cycles. The story is more complicated in the symmetric case and the vacuum expectation value does not exhibit factorization.

2000

Abstract: According to the AdS/CFT correspondence, the d = 4, N = 4 SU(N) super Yang-Mills theory is dual to the type IIB string theory compactified on AdS5 × S 5. Most of the tests performed so far are confined to the leading order at large N or equivalently string tree-level. To probe the correspondence beyond this leading order and obtain 1 N 2 corrections is difficult since string one-loop computations on an AdS5 × S 5 background generally are beyond feasibility. However, we will show that the chiral SU(4)R anomaly of the super YM theory provides an ideal testing ground to go beyond leading order in N. In this paper, we review and develop further our previous results [1] that the 1/N 2 corrections to the chiral anomaly on the super YM side can be exactly accounted for by the supergravity/string effective action induced at one loop. 1.

arXiv (Cornell University), 2015

Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on antide Sitter space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A K−1 superconformal field theory (SCFT) on AdS 5 × S 1 , with equal radii for AdS 5 and for S 1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS 5 ×S 5 /Z K. On R 4,1 ×S 1 , this six-dimensional theory has a 5(K − 1)-dimensional moduli space, with unbroken five-dimensional SU (K) gauge symmetry at (and only at) the origin. On AdS 5 × S 1 , the theory has a 2(K − 1)dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU (K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this fivedimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS 5 whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS 5. Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional N = 2 supersymmetric SU (K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the six-dimensional N = (2, 0) theory on AdS 5 × S 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2 quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories' on AdS 5 × S 1 .

Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A K−1 superconformal field theory (SCFT) on AdS 5 ×S 1 , with equal radii for AdS 5 and for S 1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS 5 × S 5 /Z K. On R 4,1 × S 1 , this six-dimensional theory has a 5(K − 1)-dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS 5 × S 1 , the theory has a 2(K − 1)-dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS 5 whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS 5. Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional N = 2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the six-dimensional N = (2, 0) theory on AdS 5 × S 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2