Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)

TL;DR

This paper develops a non-Lorentzian version of IIB supergravity by deriving its action and symmetries through a non-relativistic string limit, introducing a polynomial realization of SL(2,R) and classifying invariants.

Contribution

It introduces a novel polynomial realization of SL(2,R) for non-Lorentzian IIB supergravity and develops a formalism to classify invariants, enabling a unique construction of the bosonic action.

Findings

Derived the non-Lorentzian IIB supergravity action and symmetries.

Established a polynomial realization of SL(2,R) and classified invariants.

Proposed a non-Lorentzian bootstrap concept for supergravity.

Abstract

We derive the action and symmetries of the bosonic sector of non-Lorentzian IIB supergravity by taking the non-relativistic string limit. We find that the bosonic field content is extended by a Lagrange multiplier that implements a restriction on the Ramond-Ramond fluxes. We show that the SL(2,R) transformation rules of non-Lorentzian IIB supergravity form a novel, nonlinear polynomial realization. Using classical invariant theory of polynomial equations and binary forms, we will develop a general formalism describing the polynomial realization of SL(2,R) and apply it to the special case of non-Lorentzian IIB supergravity. Using the same formalism, we classify all the relevant SL(2,R) invariants. Invoking other bosonic symmetries, such as the local boost and dilatation symmetry, we show how the bosonic part of the non-Lorentzian IIB supergravity action is formed uniquely from these SL(2,R) invariants. This work also points towards the concept of a non-Lorentzian bootstrap, where bosonic symmetries in non-Lorentzian supergravity are used to bootstrap the bosonic dynamics in Lorentzian supergravity, without considering the fermions.