T-duality and the exotic chiral de Rham complex
Abstract
Let Z be a principal circle bundle over a base manifold M equipped with an integral closed 3-form H called the flux. Let Z be the T-dual circle bundle over M with flux H. Han and Mathai recently constructed the Z2-graded space of exotic differential forms Ak(Z). It has an additional Z-grading such that the degree zero component coincides with the space of invariant twisted differential forms k(Z, H)T, and it admits a differential that extends the twisted differential dH = d + H. The T-duality isomorphism k(Z,H)T → k+1(Z, H)T of Bouwknegt, Evslin and Mathai extends to an isomorphism k(Z,H) → Ak+1(Z). In this paper, we introduce the exotic chiral de Rham complex Ach,H,k(Z) which contains Ak(Z) as the weight zero subcomplex. We give an isomorphism ch,H,k(Z) → Ach,H,k+1(Z) where ch,H,k(Z) denotes the twisted chiral de Rham complex of Z, which chiralizes the above T-duality map.