Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3

Abstract

We study classical open string solutions with a null polygonal boundary in AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS_n and generalized parafermions.

25 pages, 4 figures, v2: a figure and references added, minor corrections, v3: references added, minor corrections, to appear in JHEP

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Cited by in corpus (36)

• TBA equations and resurgent Quantum Mechanics
• Analytic Results for MHV Wilson Loops
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Geometric aspects of the ODE/IM correspondence
• TBA Equations and Quantization Conditions
• ODE/IM correspondence and modified affine Toda field equations
• TBA equations for the Schrödinger equation with a regular singularity
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• g-Functions and gluon scattering amplitudes at strong coupling
• T-functions and multi-gluon scattering amplitudes
• WKB periods for higher order ODE and TBA equations
• TBA for non-perturbative moduli spaces
• Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models
• Wall-crossing of TBA equations and WKB periods for the third order ODE
• ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation
• ODE/IM correspondence for affine Lie algebras: A numerical approach
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• Exact mass-coupling relation for the homogeneous sine-Gordon model
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• Review of AdS/CFT Integrability, Chapter V.3: Scattering Amplitudes at Strong Coupling
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• Strong Wilson polygons from the lodge of free and bound mesons
• On the mass-coupling relation of multi-scale quantum integrable models
• Regular Wilson loops and MHV amplitudes at weak and strong coupling
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• MHV amplitudes at strong coupling and linearized TBA equations
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• WKB analysis of the linear problem for modified affine Toda field equations
• ABJM flux-tube and scattering amplitudes
• Spiky Strings with Two Spins in AdS5
• Gluon scattering amplitudes from gauge/string duality and integrability
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM