Gauge and Topological Symmetries in the Bulk Quantization of Gauge Theories

TL;DR

This paper presents a 5-dimensional topological quantum field theory framework for gauge theories, incorporating new symmetries that ensure renormalizability and simplify complex phenomena like confinement and fermion doubling.

Contribution

It introduces an extended symmetry structure in 5D gauge theories, including a gauge BRST operator, to improve understanding and handling of renormalization and non-perturbative effects.

Findings

Symmetries lead to Ward identities ensuring renormalizability.

Simplifies conceptual issues like Gribov problem and fermion doubling.

Proposes a fermion-doubling-free lattice discretization.

Abstract

A gauge theory with 4 physical dimensions can be consistently expressed as a renormalizable topological quantum field theory in 5 dimensions. We extend the symmetries in the 5-dimensional framework to include not only a topological BRST operator S that encodes the invisibility of the "bulk" (the fifth dimension), but also a gauge BRST operator W that encodes gauge-invariance and selects observables. These symmetries provide a rich structure of Ward identities which assure the renormalizability of the theory, including non-renormalization theorems. The 5-dimensional approach considerably simplifies conceptual questions such as for instance the Gribov phenomenon and fermion doubling. A confinement scenario in the 5-dimensional framework is sketched. We detail the five-dimensional mechanism of anomalies, and we exhibit a natural lattice discretization that is free of fermion doubling.