Paper detail

Duality Invariance and Higher Derivatives

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