On mysteriously missing T-duals, H-flux and the T-duality group

TL;DR

This paper provides a formula for the topology and H-flux of T-duals in type II string theories with H-flux, addressing the mystery of missing T-duals through noncommutative topology and analyzing the T-duality group's action.

Contribution

It introduces a general formula for T-duals with H-flux and explains the missing T-duals problem using noncommutative topology, including analysis of the T-duality group.

Findings

Derived a formula for T-duals' topology and H-flux.

Solved the missing T-duals puzzle using noncommutative topology.

Analyzed the T-duality group's structure and action.

Abstract

A general formula for the topology and H-flux of the T-duals of type II string theories with H-flux on toroidal compactifications is presented here. It is known that toroidal compactifications with H-flux do not necessarily have T-duals which are themselves toroidal compactifications. A big puzzle has been to explain these mysterious ``missing T-duals'', and our paper presents a solution to this problem using noncommutative topology. We also analyze the T-duality group and its action, and illustrate these concepts with examples.