Integrable flows between exact CFTs

TL;DR

This paper constructs integrable sigma-model flows connecting exact conformal field theories, demonstrating their properties and computing beta-functions, thus advancing understanding of CFT deformations and integrability.

Contribution

It explicitly constructs integrable flows between exact CFTs, including the calculation of exact beta-functions for isotropic deformations using gravitational methods.

Findings

Constructed families of integrable sigma-model actions interpolating between CFTs.

Demonstrated integrability for isotropic deformations.

Computed exact beta-functions matching previous perturbative and symmetry-based results.

Abstract

We explicitly construct families of integrable $\sigma$-model actions smoothly interpolating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels $k_1$ and $k_2$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels $k_1$ and $k_2-k_1$. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.