A No-go Theorem for a Gauge Vector as a Space-time Goldstone

TL;DR

This paper proves that it is impossible to construct healthy interacting U(1) gauge theories with vector Goldstone modes arising from non-linear space-time symmetry extensions, unlike scalar or fermion cases.

Contribution

It classifies extensions of the Poincare group and demonstrates a no-go theorem for gauge vectors as space-time Goldstone modes.

Findings

No healthy interacting U(1) gauge theories from non-linear space-time symmetries.

Scalar and fermion Goldstones can arise from symmetry extensions, but not vectors.

Soft limits of gauge vectors like Born-Infeld cannot be explained by space-time symmetries.

Abstract

Scalars and fermions can arise as Goldstone modes of non-linearly realised extensions of the Poincare group (with important implications for the soft limits of such theories): the Dirac-Born-Infeld scalar realises a higher-dimensional Poincare symmetry, while the Volkov-Akulov fermion corresponds to super-Poincare. In this paper we classify extensions of the Poincare group which give rise to a vector Goldstone mode instead. Our main result is that there are no healthy interacting $U(1)$ gauge theories that non-linearly realise space-time symmetries beyond gauge transformations. This implies that the special soft limits of e.g. the Born-Infeld vector cannot be explained by space-time symmetries.