Killings, Duality and Characteristic Polynomials

TL;DR

This paper explores the geometric framework of abelian T-duality using new tools, enabling explicit computation of characteristic polynomials and providing a simple proof of a key invariance property related to isometries without fixed points.

Contribution

It introduces a reduced formalism for abelian T-duality, allowing explicit calculation of invariant polynomials and a straightforward proof of top form invariance under certain isometries.

Findings

Explicit formulas for invariant polynomials in dual models

Proof that top forms vanish when isometries lack fixed points

Development of new geometric tools for T-duality analysis

Abstract

In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved.