Duality-invariant class of two-dimensional field theories

TL;DR

This paper introduces a new class of two-dimensional field theories with deformed target spaces, exploring their dualities, algebraic structures, and renormalization group flows, revealing fixed points and free theories.

Contribution

It constructs a novel class of duality-invariant 2D theories with deformed coset targets and analyzes their algebraic structures and RG flows.

Findings

Target spaces can reduce to cosets in the UV

Existence of fixed points where theories become free

Models exhibit non-polynomial functional generators

Abstract

We construct a new class of two-dimensional field theories with target spaces that are finite multiparameter deformations of the usual coset G/H-spaces. They arise naturally, when certain models, related by Poisson-Lie T-duality, develop a local gauge invariance at specific points of their classical moduli space. We show that canonical equivalences in this context can be formulated in loop space in terms of parafermionic-type algebras with a central extension. We find that the corresponding generating functionals are non-polynomial in the derivatives of the fields with respect to the space-like variable. After constructing models with three- and two-dimensional targets, we study renormalization group flows in this context. In the ultraviolet, in some cases, the target space of the theory reduces to a coset space or there is a fixed point where the theory becomes free.