# Transverse generalized metrics and 2d sigma models

## TL;DR

This paper introduces the concept of transverse generalized metrics within Courant algebroids, providing a geometric framework for string theory dynamics and gauging procedures.

## Contribution

It reformulates compatibility conditions between generalized metrics and Dirac structures using Dirac geometry, extending the understanding of string phase space dynamics.

## Key findings

- Defines transverse generalized metrics in Courant algebroids
- Links these metrics to string phase space dynamics
- Provides a Dirac-geometric reformulation of gauging conditions

## Abstract

We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections in purely Dirac-geometric terms. The resulting notion, a transverse generalized metric, is also what is needed for the dynamics on the reduced phase space of a string theory.