# DFT in supermanifold formulation and group manifold as background geometry

## TL;DR

This paper develops a unified formulation of Double Field Theory (DFT) using pre-QP-manifolds, integrating background geometry and consistency conditions, and applies it to DFT on group manifolds.

## Contribution

It introduces a pre-QP-manifold framework to unify DFT's consistency conditions and background geometry, including applications to group manifolds.

## Key findings

- Unified section condition and closure constraint via weak master equation
- Characterized Bianchi identities through pre-Bianchi identity
- Formulated background metric and connections using covariantized pre-QP-manifold

## Abstract

We develop the formulation of DFT on pre-QP-manifold. The consistency conditions like section condition and closure constraint are unified by a weak master equation. The Bianchi identities are also characterized by the pre-Bianchi identity. Then, the background metric and connections are formulated by using covariantized pre-QP-manifold. An application to the analysis of the DFT on group manifold is given.