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

TL;DR

This work analyzes spontaneous BRST and gauge symmetry breaking in four-dimensional topological Yang-Mills theories by coupling to Higgs-like Fujikawa-Higgs fields. It shows that adjoint-field TYMH theories develop mass scales and BRST instability beyond tree level, while realified fundamental TYMH theories attain tree-level instability with a distinct so(2N) → so(2N−2) breaking pattern, indicating local degrees of freedom in the Higgs phases. Quantum effects drive vacua localization onto flat connections and stabilize certain topological solitons, aligning with Coleman–Weinberg-type dynamics in the adjoint case. The results suggest a bridge between higher-dimensional topological gravity models and lower-energy geometrodynamics, and provide rare instances of BRST breaking in non-Abelian theories with trivial Gribov problems. Overall, the paper extends the understanding of how topological gauge theories can acquire non-topological features through Higgs-sector couplings, challenging the notion of purely topological dynamics in these systems.

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.