Gauge Field Improvement,Form-Scalar Duality and Conformal Invariance

TL;DR

This paper investigates how to preserve scale and conformal invariance in N-form gauge theories away from their critical dimension, revealing a duality with scalar theories that maintains conformal invariance through improved stress tensors.

Contribution

It demonstrates a duality between N-form gauge theories and scalar theories at specific dimensions, enabling the construction of conformally invariant stress tensors.

Findings

Conformal invariance is preserved at dimension d=N+2 via duality.

Improved stress tensors can be constructed that respect gauge and conformal invariance.

Scalar correlators, including trace anomalies, are reproduced in the dual gauge theory.

Abstract

The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d=2(N+1) is analyzed.We first exhibit the underlying group-theoretical clash between locality,gauge,Lorentz and conformal invariance require- ments. "Improved" traceless stress tensors are then constructed;each violates one of the above criteria.However,when d=N+2,there is a duality equivalence between N-form models and massless scalars.Here we show that conformal invariance is not lost,by constructing a quasilocal gauge invariant improved stress tensor.The correlators of the scalar theory are then reproduced,including the latter's trace anomaly.