On String S-matrix, Bound States and TBA

Abstract

The study of finite J effects for the light-cone AdS superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The S-matrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror S-matrix fixes the S-matrices of both theories essentially uniquely. The resulting string S-matrix S(z_1,z_2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2^{M-1} solutions of the M-particle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they might receive a finite J correction to their energy which is complex, or the energy correction might exceed corrections arising due to finite J modifications of the Bethe equations thus making the asymptotic Bethe ansatz inapplicable.

77 pages, 6 figures, v2: the statement about the periodicity condition for mirror fermions corrected; typos corrected; references added, v3: misprints corrected

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• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Strong coupling limit of Bethe Ansatz equations
• World-sheet scattering in AdS_5 x S^5 at two loops
• Constructing the AdS/CFT dressing factor
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix

Cited by in corpus (24)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• String hypothesis for the AdS_5 x S^5 mirror
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Quantum Deformations of the One-Dimensional Hubbard Model
• The S-matrix of String Bound States
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Twist-three at five loops, Bethe Ansatz and wrapping
• Finite-Size Effects for Dyonic Giant Magnons
• Quantum Wrapped Giant Magnon
• Finite size effects for giant magnons on physical strings
• Interacting finite-size magnons
• Comments on the Boundary Scattering Phase
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Minimal solution of the AdS/CFT crossing equation
• Fusion hierarchies for N = 4 superYang-Mills theory
• Universal blocks of the AdS/CFT Scattering Matrix
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Structure of the string R-matrix
• The Bethe Ansatz for AdS5 x S5 Bound States
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• Yangian Symmetry, S-Matrices and Bethe Ansatz for the AdS5 x S5 Superstring