Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics

Abstract

We propose, using the example of the O(4) sigma model, a general method for solving integrable two dimensional relativistic sigma models in a finite size periodic box. Our starting point is the so-called Y-system, which is equivalent to the thermodynamic Bethe ansatz equations of Yang and Yang. It is derived from the Zamolodchikov scattering theory in the cross channel, for virtual particles along the non-compact direction of the space-time cylinder. The method is based on the integrable Hirota dynamics that follows from the Y-system. The outcome is a nonlinear integral equation for a single complex function, valid for an arbitrary quantum state and accompanied by the finite size analogue of Bethe equations. It is close in spirit to the Destri-deVega (DdV) equation. We present the numerical data for the energy of various states as a function of the size, and derive the general Luscher-type formulas for the finite size corrections. We also re-derive by our method the DdV equation for the SU(2) chiral Gross-Neveu model.

51 pages, 7 figures; typos corrected, accepted for publication in JHEP

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Cited by in corpus (64)

• Integrability for the Full Spectrum of Planar AdS/CFT II
• Quasilocal charges in integrable lattice systems
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Y-system for Scattering Amplitudes
• String hypothesis for the AdS_5 x S^5 mirror
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• T-systems and Y-systems in integrable systems
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Superuniversality of superdiffusion
• String-charge duality in integrable lattice models
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Five-loop Konishi from the Mirror TBA
• Analytic Solution of Bremsstrahlung TBA
• Solving the AdS/CFT Y-system
• Exploring the mirror TBA
• Y-system and Quasi-Classical Strings
• Twist-three at five loops, Bethe Ansatz and wrapping
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• Wronskian Solution for AdS/CFT Y-system
• Konishi operator at intermediate coupling
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Multiple zeta functions and double wrapping in planar N=4 SYM
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Quantum integrability and functional equations
• Temperature quantization from the TBA 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
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• Discrete Hirota dynamics for AdS/CFT
• Hybrid-NLIE for the AdS/CFT spectral problem
• Finite Size Spectrum of SU(N) Principal Chiral Field from Discrete Hirota Dynamics
• Review of AdS/CFT Integrability, Chapter III.5: Luscher corrections
• On wrapping corrections to GKP-like operators
• TBA Equations and Quantization Conditions
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• Hybrid NLIE for the Mirror AdS_5 x S^5
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• A next-to-leading Luescher formula
• Numerical results for the exact spectrum of planar AdS4/CFT3
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
• Quantum transfer-matrices for the sausage model
• Integrable Field Theories with an Interacting Massless Sector
• Winding vacuum energies in a deformed O(4) sigma model
• Konishi at strong coupling from ABE
• Y-system for Z_S Orbifolds of N=4 SYM
• Double-Scaling Limit in Principal Chiral Model: a New Non-Critical String?
• Quasi-local formulation of the mirror TBA
• Unified approach to the SU(2) Principal Chiral Field model at Finite Volume
• T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras
• An inhomogeneous Lax representation for the Hirota equation
• Integrable systems and AdS/CFT duality
• Contour deformation trick in hybrid NLIE
• Casimir squared correction to the standard rotator Hamiltonian for the O($n$) sigma-model in the delta-regime
• Wrapping effects in supersymmetric gauge theories
• Spectral curve for gamma-deformed AdS/CFT
• Particles in finite volumes and a toy model of decaying neutrons
• On the rotator Hamiltonian for the SU$(N)\times$SU$(N)$ sigma-model in the delta-regime