${\cal N}=1$ supersymmetry and Non-Riemannian Double Field Theory

TL;DR

This paper develops an ${ m N}=1$ supersymmetric extension of Double Field Theory that unifies Riemannian and non-Riemannian geometries, incorporating fermions and exploring implications for supergravity and duality-related geometries.

Contribution

It introduces a unified supersymmetric framework for Riemannian and non-Riemannian Double Field Theory, including fermions and a bigravity structure, and applies it to torsional Newton-Cartan and related geometries.

Findings

Constructed ${ m N}=1$ supersymmetric DFT for various geometries.

Developed a formalism to include fermions without gauge fixing of double Lorentz symmetry.

Applied the framework to torsional Newton-Cartan and Carrollian geometries.

Abstract

We construct the ${\cal N}=1$ supersymmetric extension of Double Field Theory for Riemannian and the non-Riemannian in a unified approach. The inclusion of fermions in the double geometry force us to use the generalized frame formalism to construct the generalized flux components for these geometries. We focus on the most general prescription required to get the $D=10$ minimal supergravity model. We study how to consistently avoid the gauge fixing procedure of the double Lorentz symmetry when $n=\bar n$ and $0\le n \le 5$, which gives rise to a bigravity structure (pair of vielbeins producing the same non-Riemannian degrees of freedom). As an example we show how to to include fermionic degrees of freedom in the type I torsional Newton-Cartan (TNC) theory ($n=\bar n=1$) which is related to Carrollian geometries and stringy Newton Cartan through duality rotations and/or null reductions/uplifts.