Four-dimensional topological Yang-Mills-Higgs theories with BRST instability

TL;DR

This paper explores four-dimensional topological Yang-Mills-Higgs theories, revealing BRST instabilities and the emergence of local degrees of freedom, with implications for topological gravity models and non-Abelian gauge theories.

Contribution

It demonstrates the presence of BRST instability in coupled topological Yang-Mills-Higgs theories and analyzes their implications for physical spectra and gravity models.

Findings

BRST instability resembles Coleman-Weinberg mechanism

Stable topological solitons are present in the adjoint case

Realification leads to pronounced instability at tree-level

Abstract

We show that four-dimensional topological Yang-Mills theories, when suitably coupled to Higgs-like fields, admit representations in terms of massive gauge fields in a non-trivial neighborhood of the minima moduli. In the adjoint representation, BRST instability is present beyond tree-level, and closely resembles the Coleman-Weinberg mechanism. The fundamental representation requires realification $SU(N) \hookrightarrow SO(2N)$, but exhibits a more pronounced instability at tree-level. Stable topological solitons (vertices/monopoles) are generically present in the adjoint case. These instabilities indicate the reintroduction of local degrees of freedom into the physical spectrum of these topological field theories. In particular, the realified fundamental case may provide a promising framework for 4d topological gravity models. In addition, our results offer rare examples of BRST symmetry breaking in non-Abelian gauge theories with trivial Gribov problems.