Revisit of renormalization of Einstein-Maxwell theory at one-loop

TL;DR

This paper revisits the one-loop renormalization of the Einstein-Maxwell system, addressing gauge dependence issues, applying a refined background field method, and explicitly computing the beta function for the vector coupling.

Contribution

It introduces a systematic renormalization approach for Einstein-Maxwell theory using a refined background field method, clarifies gauge independence, and computes the vector coupling's beta function.

Findings

Successful renormalization of cosmological and Newton's constants.

Explicit calculation of the one-loop beta function for the vector coupling.

Resolution of gauge choice-dependence in the effective action.

Abstract

In a series of recent works based on foliation-based quantization in which renormalizability has been achieved for the physical sector of the theory, we have shown that the use of the standard graviton propagator interferes, due to the presence of the trace mode, with the 4D covariance. A subtlety in the background field method also requires careful handling. This status of the matter motivated us to revisit an Einstein-scalar system in one of the sequels. Continuing the endeavors, we revisit the one-loop renormalization of an Einstein-Maxwell system in the present work. The systematic renormalization of the cosmological and Newton's constants is carried out by applying the refined background field method. One-loop beta function of the vector coupling constant is explicitly computed and compared with the literature. The longstanding problem of gauge choice-dependence of the effective action is addressed and the manner in which the gauge-choice independence is restored in the present framework is discussed. The formalism also sheds light on background independent analysis. The renormalization involves a metric field redefinition originally introduced by `t Hooft; with the field redefinition the theory should be predictive.