Consistent Four-derivative Heterotic Truncations and the Kerr-Sen Solution

Four-derivative heterotic supergravity (without gauge fields) reduced on a $p$-dimensional torus leads to half-maximal supergravity coupled to $p$ vector multiplets, and it is known that removing the vector multiplets is a consistent truncation of the theory. We find a new consistent truncation of four-derivative heterotic supergravity on a torus that keeps the vector multiplets and precisely reproduces the bosonic action of heterotic supergravity (with heterotic gauge fields). We show that both truncations have an $O(d+p,d)$ symmetry when reduced on a $d$-dimensional torus and demonstrate how this embeds in the $O(d+p,d+p)$ symmetry that one gets from reducing on a $(d+p)$-dimensional torus without truncation. We then use our new truncation to obtain four-derivative corrections to the Kerr-Sen solution and compute thermodynamic quantities and multipole moments. Finally, we compare the Kerr-Sen solutions of the actions corresponding to the two different choices of truncation with the Kerr solution, the Kerr-Newman solution, and each other, and show that they have distinct four-derivative multipole structures.