Proof of the Gauge Independence of the Conformal Anomaly of Bosonic String in the Sense of Kraemmer and Rebhan

TL;DR

This paper critically examines and corrects previous claims about the gauge independence of the conformal anomaly in bosonic string theory, providing a rigorous proof under specific gauge conditions.

Contribution

It demonstrates the gauge independence of the conformal anomaly for certain gauge fixings, correcting earlier incorrect proofs by Kraemmer and Rebhan.

Findings

The original proof by Kraemmer and Rebhan was flawed.

Gauge independence holds for gauge fixings reducing to linearized de Donder gauge.

Similar results are shown for the Rebhan-Kraemner current anomaly.

Abstract

Kraemmer and Rebhan claimed the gauge independence of the conformal anomaly of bosonic string for various gauge fixings in the framework of the perturbation theory of two-dimensional quantum gravity. It is pointed out that their proof is wrong. The gauge independence is proved for the gauge-fixings which reduce to the linearized de Donder gauge in the flat limit of the background metric. Similar remarks are made also for the Rebhan-Kraemmer current anomaly.