Abstract

Using equations proposed by J. Suzuki we compute numerically the first three integrals of motion for N=1 supersymmetric CFT. Our computation agrees with the results of ODE-CFT correspondence which was explained in a more general context by S. Lukyanov.

Highlights

  • The present paper contains some preliminary results for a larger project which consists in computing the one-point functions for the supersymmetric sine-Gordon model generalising the results of [1,2] obtained for the sine-Gordon case

  • There is an interesting difference between the two cases: for the 6-vertex case the local observables are created by two fermions while for the 19-vertex case one has to introduce additional Kac–Moody current [3]

  • The supersymmetric sine-Gordon model (ssG) model is a simplest example of integrable model with supersymmetry

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Summary

Introduction

The present paper contains some preliminary results for a larger project which consists in computing the one-point functions for the supersymmetric sine-Gordon model (ssG) generalising the results of [1,2] obtained for the sine-Gordon case (sG). This problem is interesting because the integrable description of the space of local operators for the ssG model should be derived from that of the inhomogeneous 19-vertex Fateev–Zamolodchikov model while for the sG case it was related to the inhomogeneous 6-vertex model. In the computations of the ground state eigenvalues of the local integrals of motion the paper [6] follows the procedure proposed in [7], namely it uses the NLIE (non-linear integral equations) equations on a half-infinite interval. In the last section we explain how the eigenvalues are obtained from ODE-CFT correspondence following [12]

Supersymmetric sine-Gordon model
Suzuki equations
Numerical work
Eigenvalues of integrals from ODE-CFT correspondence
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