Novel all loop actions of interacting CFTs: Construction, integrability and RG flows

TL;DR

This paper constructs an all-loop effective action for interacting current algebra CFTs, proves integrability for two couplings, and explores RG flows and duality limits, advancing understanding of integrable conformal field theories.

Contribution

It introduces a novel all-loop effective action for interacting CFTs with multiple couplings, extending previous linear-level models and analyzing their integrability and RG flows.

Findings

Proved integrability for two-coupling models.

Derived RG flow equations for the coupled systems.

Explored non-Abelian T-duality limits and new features of the models.

Abstract

We construct the all loop effective action representing, for small couplings, simultaneously self and mutually interacting current algebra CFTs realized by WZW models. This non-trivially generalizes our previous works where such interactions were, at the linear level, not simultaneously present. For the two coupling case we prove integrability and calculate the coupled RG flow equations. We also consider non-Abelian T-duality type limits. Our models provide concrete realisations of integrable flows between exact CFTs and exhibit several new features which we discuss in detail.