Supergravity without gravity and its BV formulation
Julian Kupka, Charles Strickland-Constable, Fridrich Valach
TL;DR
The paper investigates a gravity-free dilatonic limit of 10D supergravity within a generalised geometry framework, where only the dilaton $\sigma$ and dilatino $\rho$ remain dynamical. It formulates the theory on a Courant algebroid, derives a complete BV action $S_{BV}$ to all orders in fermions, and analyzes its symmetries, degrees of freedom, and Costello--Li twisting to BCOV-like structures. Two concrete BV realizations are developed: one from exact Courant algebroids and another from quadratic Lie algebras, illustrating how off-shell closure and higher-order antifield terms emerge in simple, finite-dimensional toy models. The results provide a controlled setting to study BV structures, symmetry algebras, and twisting mechanisms that may shed light on aspects of the full, physical supergravity theory.
Abstract
The generalised-geometric formulation of 10-dimensional supergravity suggests a particular simple "limit", which results in a theory whose only dynamical degrees of freedom are the dilaton and the dilatino. The theory is still invariant both under generalised diffeomorphisms and a local supersymmetry and in many aspects is structurally similar to the original supergravity, which makes it a convenient playground for understanding more subtle aspects of the full physical setup. In particular, the simplicity and the geometric nature of the dilatonic theory allow us to build a full BV extension to all orders in the fermionic variables.