Vanishing of the conformal anomaly for strings in a gravitational wave

TL;DR

This paper shows that the conformal anomaly for bosonic strings in specific gravitational wave backgrounds can vanish at two loops and potentially at all orders, using a non-symmetric connection approach.

Contribution

It introduces a method to demonstrate anomaly cancellation for strings in gravitational wave backgrounds at higher loop levels.

Findings

Conformal anomaly vanishes at two-loop level in chosen backgrounds.

Under certain conditions, anomaly vanishes at all orders.

The non-symmetric-connection approach is effective for this analysis.

Abstract

Using the non-symmetric-connection approach proposed by Osborn, we demonstrate that, for a bosonic string in a specially chosen plane-fronted gravitational wave and an axion background, the conformal anomaly vanishes at the two-loop level. Under some conditions, the anomaly vanishes at all orders.