Vector fields, RG flows and emergent gauge symmetry

TL;DR

This paper analyzes the renormalization group flows of a general vector field theory with SU(N) symmetry, revealing fixed points, including emergent gauge symmetry akin to Yang-Mills, and explores their properties in the large-N limit.

Contribution

It provides a comprehensive 1-loop RG flow analysis of a general vector field theory with global SU(N) symmetry, identifying fixed points and emergent gauge symmetry scenarios.

Findings

Existence of asymptotically free RG flows with non-trivial fixed points.

Yang-Mills theory emerges at a specific fixed point.

Other fixed points are gauge symmetry violating perturbations.

Abstract

We consider the most general perturbatively renormalizable theory of vector fields in four dimensions with a global SU(N) symmetry and massless couplings. The Lagrangian contains 1 quadratic, 2 cubic and 4 quartic couplings. The RG flow among this set of 7 couplings is computed to 1-loop and a rich phase diagram is mapped out; in particular it is shown that a finite number of asymptotically free RG-flows exist corresponding to non-trivial fixed points for the ratios of the couplings. None of these are gauge theories, i.e. possess only global SU(N) invariance but not a local one. We also include the most general ghost couplings, still with global SU(N) invariance, and compute the RG flow to 1-loop for all 9 resulting couplings. Again asymptotically free RG flows exist with non-trivial fixed points for the ratios of couplings. It is shown that Yang-Mills theory emerges at a particular fixed point. The theories at the other fixed points are marginally relevant gauge symmetry violating perturbations of Yang-Mills theory. The large-N limit is also investigated in detail.