Exploring the mirror TBA

Abstract

We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N=4 SYM operators from the sl(2) sector. We show that each state/operator is described by its own set of TBA equations. Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant λ, and the excited states integral equations have to be modified each time one crosses one of those. In particular, estimation based on the large L asymptotic solution gives λ\approx 774 for the first critical value corresponding to the Konishi operator. Our results indicate that the related calculations and conclusions of Gromov, Kazakov and Vieira should be interpreted with caution. The phenomenon we discuss might potentially explain the mismatch between their recent computation of the scaling dimension of the Konishi operator and the one done by Roiban and Tseytlin by using the string theory sigma model.

69 pages, v2: new "hybrid" equations for YQ-functions, figures and tables are added. Analyticity of Y-system is discussed, v3: published version

References in corpus (20)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Finite-size Effects from Giant Magnons
• On String S-matrix, Bound States and TBA
• Dressing and Wrapping
• String hypothesis for the AdS_5 x S^5 mirror
• On AdS_5 x S^5 String S-matrix
• Wrapping at four loops in N=4 SYM
• Five loop Konishi from AdS/CFT
• Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator
• Twist-three at five loops, Bethe Ansatz and wrapping
• Y-system and Quasi-Classical Strings
• Finite-Size Effects for Dyonic Giant Magnons
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Finite size effects for giant magnons on physical strings
• Temperature quantization from the TBA equations
• Five-loop anomalous dimension at critical wrapping order in N=4 SYM
• Finite-Size Effects for Multi-Magnon States
• Discrete Hirota dynamics for AdS/CFT
• Bound State Transfer Matrix for AdS5 x S5 Superstring

Cited by in corpus (54)

• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
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• Integrable Wilson loops
• Towards integrability for AdS3/CFT2
• Quantum folded string and integrability: from finite size effects to Konishi dimension
• Solving the AdS/CFT Y-system
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• The Quantum Deformed Mirror TBA I
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• 5-loop Konishi from linearized TBA and the XXX magnet
• The spectral problem for strings on twisted AdS_5 x S^5
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Twisting the Mirror TBA
• The Quantum Deformed Mirror TBA II
• Y-system and beta-deformed N=4 Super-Yang-Mills
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• The Effectiveness of Relativistic Invariance in AdS${}_3$
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• The Bajnok-Janik formula and wrapping corrections
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• Hybrid-NLIE for the AdS/CFT spectral problem
• The spectrum of tachyons in AdS/CFT
• Comments on the Mirror TBA
• Strong coupling results from the numerical solution of the quantum spectral curve
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
• Exceptional Operators in N=4 super Yang-Mills
• A next-to-leading Luescher formula
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Numerical results for the exact spectrum of planar AdS4/CFT3
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• Lifting asymptotic degeneracies with the Mirror TBA
• Non-planar anomalous dimension of twist-2 operators: higher moments at four loops
• Bound States in the Mirror TBA
• Y-system for Z_S Orbifolds of N=4 SYM
• Twist-2 at five loops: Wrapping corrections without wrapping computations
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion
• Double-logs, Gribov-Lipatov reciprocity and wrapping
• Quasi-local formulation of the mirror TBA
• Orbifolded Konishi from the Mirror TBA
• 6-loop anomalous dimension of a single impurity operator from AdS/CFT and multiple zeta values
• Integrability treatment of AdS/CFT orbifolds
• Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
• Wrapping effects in supersymmetric gauge theories
• Wrapping corrections for non-diagonal boundaries in AdS/CFT
• Contour deformation trick in hybrid NLIE
• Extensive numerical study of a D-brane, anti-D-brane system in AdS5/CFT4
• Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension
• Large spin expansion of the wrapping correction to Freyhult-Rej-Zieme twist operators
• Transfer matrices for AdS3/CFT2
• Deforming integrable models of AdS${}_3$ strings