Quantum Sine(h)-Gordon Model and Classical Integrable Equations

Abstract

We study a family of classical solutions of modified sinh-Gordon equation, $\partial_z\partial_{\bar z} η-\re^{2η}+p(z)\,p({\bar z})\ \re^{-2η}=0$ with $p(z)=z^{2\alpha }-s^{2\alpha }$. We show that certain connection coefficients for solutions of the associated linear problem coincide with the $Q$-function of the quantum sine-Gordon $(\alpha >0)$ or sinh-Gordon $(\alpha <-1)$ models.

35 pages, 3 figures

References in corpus (3)

• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Thermodynamic Bubble Ansatz
• Y-system for Scattering Amplitudes

Cited by in corpus (50)

• Form factors at strong coupling via a Y-system
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• A Shortcut to the Q-Operator
• Wall-Crossing in Coupled 2d-4d Systems
• Conserved currents and $\text{T}{\bar{\text{T}}}_s$ irrelevant deformations of 2D integrable field theories
• On one-point functions for sinh-Gordon model at finite temperature
• Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case
• Opers, surface defects, and Yang-Yang functional
• Bethe Ansatz and the Spectral Theory of affine Lie algebra--valued connections II. The non simply--laced case
• Integrability and cycles of deformed $\mathcal{N}=2$ gauge theory
• On spectrum of ILW hierarchy in conformal field theory
• Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states
• Geometric aspects of the ODE/IM correspondence
• ODE/IM correspondence and the Argyres-Douglas theory
• ODE/IM correspondence for the Fateev model
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• ODE/IM correspondence and modified affine Toda field equations
• The Bethe Ansatz and the Tzitzéica-Bullough-Dodd equation
• TBA equations for the Schrödinger equation with a regular singularity
• Bethe Ansatz equations for the classical $A_n^{(1)}$ affine Toda field theories
• Critical values of the Yang-Yang functional in the quantum sine-Gordon model
• ODE/IM correspondence and Bethe ansatz for affine Toda field equations
• WKB periods for higher order ODE and TBA equations
• Quantum transfer-matrices for the sausage model
• Opers for higher states of quantum KdV models
• Counting monster potentials
• 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
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• ODE/IM correspondence for affine Lie algebras: A numerical approach
• Resurgence, Painleve Equations and Conformal Blocks
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics
• On solutions of the Bethe Ansatz for the Quantum KdV model
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• Bukhvostov-Lipatov model and quantum-classical duality
• Vacuum energy of the Bukhvostov-Lipatov model
• Kondo line defects and affine Gaudin models
• Elementary functions in Thermodynamic Bethe Ansatz
• 3-dimensional mixed BF theory and Hitchin's integrable system
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• WKB analysis of the linear problem for modified affine Toda field equations
• Feigin-Frenkel-Hernandez Opers and the QQ-system
• Asymptotic solutions for linear ODEs with not-necessarily meromorphic coefficients: a Levinson type theorem on complex domains, and applications
• From Fuchsian differential equations to integrable QFT
• Integrals of motion in $W{E}_6$ CFT and the ODE/IM correspondence
• The ODE/IM Correspondence between $C(2{)}^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT
• On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model
• A short review on TBA equation and scattering amplitude/Wilson loop duality