Gauge-Fixing and Residual Symmetries in Gauge/Gravity Theories with Extra Dimensions

TL;DR

This paper explores residual quantum symmetries in gauge/gravity theories with extra dimensions, demonstrating their role in gauge-fixing independence and providing new insights into the vDVZ-discontinuity.

Contribution

It introduces a novel analysis of residual SUSY-like symmetries in compactified theories and proposes a new gauge choice for higher-dimensional gravity, confirming gauge independence of physical amplitudes.

Findings

Residual symmetries are generated by quantum supercharges.

Gauge independence of graviton exchange amplitude is confirmed.

A supersymmetric interpretation of the vDVZ-discontinuity is provided.

Abstract

We study compactified pure gauge/gravitational theories with gauge-fixing terms and show that these theories possess quantum mechanical SUSY-like symmetries between unphysical degrees of freedom. These residual symmetries are global symmetries and generated by quantum mechanical N=2 supercharges. Also, we establish new one-parameter family of gauge choices for higher-dimensional gravity, and calculate as a check of its validity one graviton exchange amplitude in the lowest tree-level approximation. We confirm that the result is indeed $\xi$-independent and the cancellation of the $\xi$-dependence is ensured by the residual symmetries. We also give a simple interpretation of the vDVZ-discontinuity, which arises in the lowest tree-level approximation, from the supersymmetric point of view.