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 ${\alpha }^{\prime }$. 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 ${\alpha }^{\prime }$-corrections through a Green-Schwarz type mechanism. We prove that, up to a global pre-factor, the first order ${\alpha }^{\prime }$-corrections are uniquely determined by $\mathrm{O}(d,d,\mathbb{R})$ invariance.

41 pages. v2: references added, minor changes