Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation

Abstract

We study line operators in the two-dimensional sigma-model on PSl(n|n) using the current-current OPEs. We regularize and renormalize these line operators, and compute their fusion up to second order in perturbation theory. In particular we show that the transfer matrix associated to a one-parameter family of flat connections is free of divergences. Moreover this transfer matrix satisfies the Hirota equation (which can be rewritten as a Y-system, or Thermodynamic Bethe Ansatz equations) for all values of the two parameters defining the sigma-model. This provides a first-principles derivation of the Hirota equation which does not rely on the string hypothesis nor on the assumption of quantum integrability.

53 pages, 6 figures. Minor corrections

References in corpus (11)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• String hypothesis for the AdS_5 x S^5 mirror
• Fusion of conformal interfaces
• S-matrix for magnons in the D1-D5 system
• From Characters to Quantum (Super)Spin Chains via Fusion
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• Finite Size Spectrum of SU(N) Principal Chiral Field from Discrete Hirota Dynamics
• Perturbative study of the transfer matrix on the string worldsheet in AdS(5)xS(5)
• Quantization of Wilson loops in Wess-Zumino-Witten models

Cited by in corpus (19)

• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• Integrability, spin-chains and the AdS3/CFT2 correspondence
• Solving the AdS/CFT Y-system
• 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.7: Hirota Dynamics for Quantum Integrability
• Superstrings in AdS
• Fusion of Critical Defect Lines in the 2D Ising Model
• Massless particles on supergroups and AdS3 x S3 supergravity
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Harmonic Superspace from the $Ad{S}_5\times S^5$ Pure Spinor Formalism
• First-principles derivation of the AdS/CFT Y-systems
• On the quantization of continuous non-ultralocal integrable systems
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• On the equivalence theorem for integrable systems
• Integrable theories and generalized graded Maillet algebras
• The r-matrix of the Alday-Arutyunov-Frolov model
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• Non-chiral current algebras for deformed supergroup WZW models
• Yangian Superalgebras in Conformal Field Theory