The a-theorem for the four-dimensional gauged vector model

TL;DR

This paper investigates the a-theorem in four-dimensional conformal field theories by analyzing a gauged vector model coupled with the Banks-Zaks model, confirming the monotonic decrease of the a-anomaly between fixed points.

Contribution

It provides an explicit example of the a-theorem in an interacting four-dimensional gauge theory using a leading order 1/N expansion and all orders in coupling.

Findings

The model exhibits both IR and UV fixed points.

The a-anomaly decreases from UV to IR fixed point.

The a-theorem holds in this gauged vector model context.

Abstract

The discussion of renormalization group flows in four-dimensional conformal field theories has recently focused on the a-anomaly. It has recently been shown that there is a monotonic decreasing function which interpolates between the ultraviolet and infrared fixed points such that \Delta a = a_UV - a_IR > 0. The analysis has been extended to weakly relevant and marginal deformations, though there are few explicit examples involving interacting theories. In this paper we examine the a-theorem in the context of the gauged vector model which couples the usual vector model to the Banks-Zaks model. We consider the model to leading order in the 1/N expansion, all orders in the coupling constant \lambda, and to second order in g^2. The model has both an IR and UV fixed point, and satisfies \Delta a > 0.