Extended Conformal Symmetry in $d\neq 4$: Conformal Symmetry of Abelian Gauge Theory in the Physical Sector

TL;DR

This paper introduces a non-local, gauge-invariant extension of the special conformal transformation that restores conformal symmetry in the physical sector of Abelian gauge theories in dimensions other than four.

Contribution

It constructs a novel non-local conformal symmetry compatible with gauge invariance and BRST formalism, applicable to Maxwell theory in any dimension $d eq 4$.

Findings

The extended transformation preserves gauge-invariant correlators and equations of motion.

Maxwell theory remains invariant under the new symmetry in $d eq 4$.

The work demonstrates the explicit invariance of the theory's key physical quantities.

Abstract

Abelian gauge theory in $d\neq 4$ spacetime dimensions is an example of a scale invariant theory which does not possess conformal symmetry -- the special conformal transformation(SCT) explicitly breaks the gauge invariance of the theory. In this work, we construct a non-local gauge-invariant extension of the SCT, which is compatible with the BRST formalism and defines a new symmetry of the physical Hilbert space of the Maxwell theory for any dimension $d\geqslant 3$. We prove the invariance of the Maxwell theory in $d\geqslant 3$ by explicitly showing that the gauge-invariant two-point correlation functions, the action, and the classical equation of motion are unchanged under such a transformation.