Old Dualities and New Anomalies

TL;DR

This paper investigates the symmetry properties of string worldsheet theories, demonstrating that while an O(d,d) symmetry can be formulated, it is anomalous due to chiral bosons and requires a Green-Schwarz mechanism for cancellation.

Contribution

The authors provide a consistent O(d,d,R) invariant formulation of the worldsheet theory, including all target space fields, and analyze the anomaly caused by chiral bosons.

Findings

The worldsheet theory is not O(d,d,R) invariant unless winding and momentum are zero.

A Green-Schwarz mechanism cancels the O(d,d) anomaly.

A generalized O(d,d,R) invariant action is constructed.

Abstract

We revisit the question whether the worldsheet theory of a string admits a global O(d,d) symmetry. We consider the truncation of the target space theory in which fields are independent of d coordinates, which is O(d,d,R) invariant. The worldsheet theory is not O(d,d,R) invariant, unless it is truncated by setting winding and center-of-mass momenta to zero. We prove consistency of this truncation and give a manifestly O(d,d,R) invariant action, generalizing a formulation due to Tseytlin by including all external and internal target space fields. It is shown that, due to chiral bosons, this symmetry is anomalous. The anomaly is cancelled by a Green-Schwarz mechanism that utilizes the external B-field.