Deformations of duality-symmetric theories

TL;DR

This paper demonstrates that free duality-symmetric actions cannot be consistently deformed to include non-Abelian interactions within local, covariant frameworks, indicating the need for alternative approaches for non-Abelian duality theories.

Contribution

It proves the non-existence of consistent, local, and covariant self-interactions deforming free duality-symmetric actions, especially non-Abelian ones, within standard perturbative field theory.

Findings

Non-Abelian deformations are not allowed in duality-symmetric theories.

Sum of free actions cannot be consistently deformed with local self-interactions.

Analyticity of self-interactions for a single duality-symmetric gauge field is analyzed.

Abstract

We prove that a sum of free non-covariant duality-symmetric actions does not allow consistent, continuous and local self-interactions that deform the gauge transformations. For instance, non-Abelian deformations are not allowed, even in 4 dimensions where Yang-Mills type interactions of 1-forms are allowed in the non-manifestly duality-symmetric formulation. This suggests that non-Abelian duality should require to leave the standard formalism of perturbative local field theories. The analyticity of self-interactions for a single duality-symmetric gauge field in four dimensions is also analyzed.