Green-Schwarz Mechanism for String Dualities
Camille Eloy, Olaf Hohm, Henning Samtleben
Abstract
We determine the complete spacetime action to first order in ${\ensuremath{\alpha}}^{\ensuremath{'}}$ 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 ${\ensuremath{\alpha}}^{\ensuremath{'}}$-deformed $\mathrm{O}(d,d,\mathbb{R})$ transformations. In terms of a frame formalism with $\mathrm{GL}(d)\ifmmode\times\else\texttimes\fi{}\mathrm{GL}(d)$ gauge symmetry this amounts to a modification of the three-form curvature by a Chern-Simons term for composite gauge fields.