Weyl Anomalies of Strings in Temporal Gauge

TL;DR

This paper analyzes Weyl anomalies in string theory within the temporal gauge, demonstrating explicit metric integration and questioning the determination of critical dimensions in this gauge.

Contribution

It provides an explicit integration method for the metric in temporal gauge and challenges the conventional understanding of critical dimensions in string theory.

Findings

Explicit metric integration in temporal gauge

Critical dimensions may not be fixed in this gauge

Implications for string theory anomalies

Abstract

We consider two-dimensional quantum gravity coupled to matter in the temporal gauge, using the Polyakov path integral. We show that the integration over the metric can be explicitly performed under some plausible assumptions. We also discuss that the critical dimensions in string theory may not be determined in the temporal gauge.