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On the spectrum of the Sinh-Gordon model in finite volume

J. Teschner

Abstract

We derive a characterization of the spectrum of the Sinh-Gordon model in terms of certain nonlinear integral equations. There exists a large class of solutions to these equations which allows a continuation between the infrared and the ultraviolet limits, respectively. We present nontrivial evidence for the claim that the class of solutions in question describes the spectrum of the Sinh-Gordon model completely in both of these limits. The evidence includes some nontrivial relations to Liouville theory.

On the spectrum of the Sinh-Gordon model in finite volume

Abstract

We derive a characterization of the spectrum of the Sinh-Gordon model in terms of certain nonlinear integral equations. There exists a large class of solutions to these equations which allows a continuation between the infrared and the ultraviolet limits, respectively. We present nontrivial evidence for the claim that the class of solutions in question describes the spectrum of the Sinh-Gordon model completely in both of these limits. The evidence includes some nontrivial relations to Liouville theory.

Paper Structure

This paper contains 36 sections, 7 theorems, 112 equations.

Table of Contents

  1. Introduction
  2. Lattice Sinh-Gordon model
  3. Definition of the lattice Sinh-Gordon model
  4. Hilbert space ${\mathcal{H}}$
  5. Conserved charges
  6. Hamiltonian
  7. Characterization of the spectrum
  8. Quantization conditions
  9. SOV representation
  10. Reformulation in terms of integral equations
  11. The integral equations
  12. The correspondence
  13. Continuum Sinh Gordon model
  14. Continuum limit
  15. Reformulation in terms of the Baxter equation
  16. ...and 21 more sections

Key Result

Proposition 1

$q(u)$ satisfies the so-called quantum Wronskian condition, where we have used the notations $\delta'\equiv \delta-b$ and with

Theorems & Definitions (21)

  • Claim 1
  • Conjecture 1
  • Claim 2
  • Proposition 1
  • Claim 3
  • Definition 1
  • Claim 4
  • Proposition 2
  • proof
  • Conjecture 2
  • ...and 11 more