T-Duality and Lie bi-algebroid structures

TL;DR

This paper reveals that the geometric duality in T-duality between string theories on different manifolds is fundamentally described by Lie bialgebroid structures, connecting string theory dualities with advanced geometric algebra.

Contribution

It establishes a precise mathematical correspondence between T-duality in string theory and Lie bialgebroid structures, clarifying the geometric nature of dualities.

Findings

T-duality corresponds to Lie bialgebroid structures

Provides a geometric interpretation of T-duality

Bridges string theory dualities with Lie algebroid theory

Abstract

We show that the geometric notion of duality behind $T$-duality, between two string theories on different manifolds $E, \hat{E}$ in the sense of \cite{BHM1}\cite{BHM2}, is precisely that of Lie bialgebroids due to Mackenzie and Xu \cite{MX}.