PSU(2,2|4) Character of Quasiclassical AdS/CFT

Abstract

We solve the recently proposed T- and Y-systems (Hirota equation) for the exact spectrum of AdS/CFT in the strong coupling scaling limit for an arbitrary quasiclassical string state. The corresponding T-functions appear to be super-characters of the SU(2,2|4) group in unitary representations with a highest weight, with the classical AdS5xS5 superstring monodromy matrix as the group element. We propose a concise first Weyl-type formula for these characters and show that they correctly reproduce the results of quasiclassical one-loop quantization in all sectors of the superstring, under some natural assumptions. We also speculate about possible relation between the T-functions and the quantum monodromy matrix.

40 pages, 6 figures; v2: minor corrections, added a brief discussion of the quantum case

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• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
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• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Quantum corrections to the string Bethe ansatz
• On String S-matrix, Bound States and TBA
• Exact AdS/CFT spectrum: Konishi dimension at any coupling
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• String hypothesis for the AdS_5 x S^5 mirror
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Wrapping interactions at strong coupling -- the giant magnon
• Five loop Konishi from AdS/CFT
• Baxter's Q-operators for supersymmetric spin chains
• Five-loop Konishi from the Mirror TBA
• Complete 1-loop test of AdS/CFT
• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)
• Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• TBA and Y-system for planar $Ad{S}_4/CF{T}_3$
• Exact expressions for quantum corrections to spinning strings
• Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• Exploring the mirror TBA
• Y-system and Quasi-Classical Strings
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• Constructing the AdS/CFT dressing factor
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• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• Five-loop anomalous dimension at critical wrapping order in N=4 SYM
• Discrete Hirota dynamics for AdS/CFT
• Quantum strings in AdS5 x S5 and AdS/CFT duality
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Cited by in corpus (52)

• Quantum spectral curve for AdS_5/CFT_4
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• A Shortcut to the Q-Operator
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Quantum folded string and integrability: from finite size effects to Konishi dimension
• Solving the AdS/CFT Y-system
• Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains
• Wronskian Solution for AdS/CFT Y-system
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• Konishi operator at intermediate coupling
• Multiple zeta functions and double wrapping in planar N=4 SYM
• Classical tau-function for quantum spin chains
• Quantum integrability and functional equations
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• Twisted Bethe equations from a twisted S-matrix
• Yangians, S-matrices and AdS/CFT
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz
• Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability
• The Bajnok-Janik formula and wrapping corrections
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• Hybrid-NLIE for the AdS/CFT spectral problem
• Finite Size Spectrum of SU(N) Principal Chiral Field from Discrete Hirota Dynamics
• The Hagedorn temperature of AdS5/CFT4 via integrability
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• Quantum folded string in S^5 and the Konishi multiplet at strong coupling
• Hybrid NLIE for the Mirror AdS_5 x S^5
• Colour-Twist Operators I: Spectrum and Wave Functions
• A next-to-leading Luescher formula
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Y-system for Y=0 brane in planar AdS/CFT
• First-principles derivation of the AdS/CFT Y-systems
• Numerical results for the exact spectrum of planar AdS4/CFT3
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Supersymmetric quantum spin chains and classical integrable systems
• Quasi-local formulation of the mirror TBA
• The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
• Finite-size effects of beta-deformed AdS_5/CFT_4 at strong coupling
• Spectral curve for open strings attached to the Y=0 brane
• Integrability treatment of AdS/CFT orbifolds
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• Drinfeld basis for string-inspired Baxter operators
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Positive Energy Unitary Irreducible Representations of the Superalgebras $osp(1|2n,R)$ and Character Formulae
• Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
• Wrapping effects in supersymmetric gauge theories
• Extensive numerical study of a D-brane, anti-D-brane system in AdS5/CFT4
• The complete unitary dual of non-compact Lie superalgebra su(p,q|m) via the generalised oscillator formalism, and non-compact Young diagrams
• Spectral curve for gamma-deformed AdS/CFT