Second order bosonic string effective action from $O(d,d)$

Abstract

The corrections to the tree-level effective action for the bosonic string up to second order in $\hat{I}{\pm }^{\prime }$ are fixed by requiring its dimensional reduction to $26-d$ dimensions to be compatible with $O(d,d)$ symmetry. The result is in agreement with the literature, but takes a simpler form than previously know expressions. We identify some structures in the Lagrangian which appear at least at the first three orders in $\hat{I}{\pm }^{\prime }$.

21+8 pages; v2: Minor clarifications, published version