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

TL;DR

The paper shows that heterotic supergravity reduced on a torus admits two distinct four-derivative consistent truncations, including a new one that retains gauge fields and fits into an $O(d+p,d+p)$ framework. By applying an $O(2,1)$ boost within each truncation, the authors construct four-derivative Kerr-Sen solutions, derive their thermodynamics and multipole moments, and demonstrate that these solutions have four-derivative structures that are distinct from Kerr and Kerr-Newman, as well as from each other. The results rely on a careful embedding of the truncations into the full duality group and a five-dimensional uplift to implement the solution-generating technique, with charge-fixing shifts ensuring consistent boundary conditions. Collectively, the work reveals rich higher-derivative phenomenology in heterotic gravity and provides a concrete, testable distinction between different truncation schemes via multipole moments.

Abstract

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.

Figures (2)

• Figure 1: The $(+)$- and $(-)$-truncations restrict us to two $O(d+p,d)$ subgroups of $O(d+p,d+p)$, while a similarity transformation with $U$ provides an isomorphism between them.
• Figure 2: A schematic depiction of the series of uplifts, field redefinitions, and transformations we perform to obtain the Kerr-Sen solution.