The non-Abelian Duality Problem

TL;DR

This paper introduces a new theory of duality transformations that enables the construction of dual representations for models with non-Abelian symmetries, solving a long-standing problem in the field.

Contribution

It develops a generalized duality framework that encompasses traditional and non-Abelian dualities, expanding the scope of duality applications in theoretical models.

Findings

Successfully constructs dual representations for non-Abelian models.

Shows that symmetry group type (Abelian or not) is irrelevant for duality transformations.

Extends duality theory to include more general transformations.

Abstract

We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that hinges on two key observations: (i) from the point of view of dualities, whether the group of symmetries of a model is or is not Abelian is unimportant, and (ii) the new theory of dualities that we exploit includes traditional duality transformations, but also introduces in a natural way more general transformations.