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 $O(d,d,\mathbb{R})$ invariant. The worldsheet theory is not $O(d,d,\mathbb{R})$ 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 $O(d,d,\mathbb{R})$ 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.

• Received 29 September 2020
• Accepted 19 October 2020

DOI:https://doi.org/10.1103/PhysRevD.102.126002

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Published by the American Physical Society