Green-Schwarz Mechanism for String Dualities

Abstract

We determine the complete spacetime action to first order in ${\alpha }^{\prime }$ for the massless fields of bosonic string theory compactified on a $d$-dimensional torus. A fully systematic procedure is developed that brings the action into a minimal form in which all fields apart from the metric enter only with first-order derivatives. T-duality implies that this action must have a global $\mathrm{O}(d,d,\mathbb{R})$ symmetry, and we show that this requires a Green-Schwarz type mechanism for ${\alpha }^{\prime }$-deformed $\mathrm{O}(d,d,\mathbb{R})$ transformations. In terms of a frame formalism with $\mathrm{GL}(d)\times \mathrm{GL}(d)$ gauge symmetry this amounts to a modification of the three-form curvature by a Chern-Simons term for composite gauge fields.

9 pages, v2: some corrected typos and corrected Eq. (12). Published version