The $H$-flux on flag manifolds generated by infinitesimal $T$-duality

TL;DR

This paper introduces a new correspondence involving flag manifolds and $H$-flux, showing how infinitesimal $T$-duality can generate flux and exchange complex and symplectic structures through $B$-transformations.

Contribution

It develops a novel framework linking flag manifolds with $H$-flux via infinitesimal $T$-duality, expanding understanding of flux generation and structure exchange.

Findings

Infinitesimal $T$-duality can produce nontrivial $H$-flux from fluxless pairs.

The correspondence exchanges complex and symplectic structures up to $B$-transformations.

The framework broadens the geometric understanding of fluxes on flag manifolds.

Abstract

We define a new correspondence for pairs $(\mathbb{F},H)$ formed by a flag manifold $\mathbb{F}$ together with an $H$-flux on $\mathbb{F}$. Given its role within our correspondence, infinitesimal $T$-duality may be viewed as a source of $H$-flux, in the sense that it contributes towards taking fluxless pairs $(\mathbb{F},0)$ to pairs $(\mathbb{F}^\vee, H^\vee)$ carrying nontrivial flux $H^\vee\neq 0$. We also illustrate how our correspondence exchanges complex structures with symplectic ones up to $B$-transformations.