2025/04/29 by Han, Fei, Mathai, Varghese
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2504.20358
The main purpose of this paper is to establish the loop space formulation of T-duality in the presence of background flux. In particular, we construct a loop space analogue of the Hori formula, termed the loop Hori map, and demonstrate that it induces a quasi-isomorphism between the exotic twisted equivariant cohomologies on the free loop spaces of the T-dual sides. Spacetime, when viewed as the constant loops, is a submanifold of loop space. The duality that we prove on loop space restricts to the T-duality with H-flux on spacetime. This significantly refines the earlier work of the authors in 2015 where T-duality was established after localisation to the base space. The construction of the loop Hori map is an application of our generalization of the Bismut--Chern character in 2015, originally introduced in the loop space interpretation of the Atiyah--Singer index theorem by Atiyah--Witten and Bismut.