Duality invariance and higher derivatives

Abstract

We dimensionally reduce the spacetime action of bosonic string theory, and that of the bosonic sector of heterotic string theory after truncating the Yang-Mills gauge fields, on a $d$-dimensional torus including all higher-derivative corrections to first order in ${\ensuremath{\alpha}}^{\ensuremath{'}}$. A systematic procedure is developed that brings this action into a minimal form in which all fields except the metric carry only first-order derivatives. This action is shown to be invariant under $\mathrm{O}(d,d,\mathbb{R})$ transformations that acquire ${\ensuremath{\alpha}}^{\ensuremath{'}}$-corrections through a Green-Schwarz type mechanism. We prove that, up to a global prefactor, the first-order ${\ensuremath{\alpha}}^{\ensuremath{'}}$-corrections are uniquely determined by $\mathrm{O}(d,d,\mathbb{R})$ invariance.

Topics & Concepts