Deformed 2d CFT: Landau-Ginzburg Lagrangians and Toda theories

TL;DR

This paper explores the relationship between affine Toda field theories and Landau-Ginzburg Lagrangians as descriptions of deformed 2d conformal field theories, highlighting quantum corrections and structural similarities.

Contribution

It demonstrates the consistency of two deformation implementations with quantum corrections and investigates the potential transformation between Lagrangians, especially in the sine-Gordon case.

Findings

Quantum corrections ensure consistency between the two descriptions.

A direct transformation exists in the sine-Gordon model but not generally.

Both potentials share similar extremal structures.

Abstract

We consider the relation between affine Toda field theories (ATFT) and Landau-Ginzburg Lagrangians as alternative descriptions of deformed 2d CFT. First, we show that the two concrete implementations of the deformation are consistent once quantum corrections to the Landau-Ginzburg Lagrangian are taken into account. Second, inspired by Gepner's fusion potentials, we explore the possibility of a direct connection between both types of Lagrangians; namely, whether they can be transformed one into another by a change of variables. This direct connection exists in the one-variable case, namely, for the sine-Gordon model, but cannot be established in general. Nevertheless, we show that both potentials exhibit the same structure of extrema.