Effective Quantum Field Theory for the Thermodynamical Bethe Ansatz

TL;DR

This paper develops an effective quantum field theory for wrapping effects in 1+1 dimensional factorised scattering models, utilizing a graph-theoretical approach to connect with thermodynamic Bethe ansatz (TBA) equations.

Contribution

It introduces a novel effective QFT framework incorporating both bosonic and fermionic fields, which is one-loop exact and localizes to TBA equations, applicable to models beyond difference form scattering matrices.

Findings

Constructed an effective QFT for wrapping effects in integrable models.

Demonstrated the one-loop exactness and localization of the path integral.

Applied the framework to models relevant for AdS/CFT correspondence.

Abstract

We construct an effective Quantum Field Theory for the wrapping effects in 1+1 dimensional models of factorised scattering. The recently developed graph-theoretical approach to TBA gives the perturbative desctiption of this QFT. For the sake of simplicity we limit ourselves to scattering matrices for a single neutral particle and no bound state poles, such as the sinh-Gordon one. On the other hand, in view of applications to AdS/CFT, we do not assume that the scattering matrix is of difference type. The effective QFT involves both bosonic and fermionic fields and possesses a symmetry which makes it one-loop exact. The corresponding path integral localises to a critical point determined by the TBA equation.