Spin-1 fields and RG flows in 4 dimensions

TL;DR

This paper constructs the most general classically scale-invariant, renormalizable Lagrangian for spin-1 fields in 4D, computes 1-loop beta functions, and identifies asymptotically free RG flows that are not gauge theories.

Contribution

It introduces a new class of non-gauge, scale-invariant spin-1 field theories with detailed RG flow analysis and large-N behavior.

Findings

Identified asymptotically free RG flows in non-gauge theories.

Computed 1-loop beta functions for a 7-coupling system.

Demonstrated similar RG phase space for all N>5, including large N.

Abstract

The most general local, classically scale invariant, perturbatively renormalizable, globally $SU(N)$ invariant Lagrangian is constructed for spin-1 fields in 4 dimensions. The total number of independent couplings is 7 and the 1-loop $\beta$-functions are computed in the MSbar scheme. A number of asymptotically free RG flows are identified corresponding to non-trivial QFTs. None of these are gauge theories. The details of the large-$N$ limit are also worked out and it is shown that the RG phase space is qualitatively similar for all $N>5$ including the $N\to\infty$ limit.