NS-NS fluxes in Hitchin's generalized geometry

TL;DR

This paper extends the concept of NS-NS flux within Hitchin's generalized geometry, providing a unified framework that encompasses various flux types and introduces a generalized connection approach.

Contribution

It introduces a generalized flux concept in Hitchin's geometry, unifying three-form, geometric, and non-geometric fluxes, and describes a new generalized connection.

Findings

Generalized flux can compute three-form, geometric, and Q-flux.

Explicit examples demonstrate the flux's computation.

A generalized connection framework explains the flux origin.

Abstract

The standard notion of NS-NS 3-form flux is lifted to Hitchin's generalized geometry. This generalized flux is given in terms of an integral of a modified Nijenhuis operator over a generalized 3-cycle. Explicitly evaluating the generalized flux in a number of familiar examples, we show that it can compute three-form flux, geometric flux and non-geometric Q-flux. Finally, a generalized connection that acts on generalized vectors is described and we show how the flux arises from it.