221 research outputs found

    Witten Genus and Elliptic genera for proper actions

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    In this paper, we construct for the first time, the Witten genus and elliptic genera on noncompact manifolds with a proper cocompact action by an almost connected Lie group and prove vanishing and rigidity results that generalise known results for compact group actions on compact manifolds. We also compute our genera for some interesting examples.Comment: 26 pages. A conjecture remove

    T-duality of current algebras and their quantization

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    In this paper we show that the T-duality transform of Bouwknegt, Evslin and Mathai applies to determine isomorphisms of certain current algebras and their associated vertex algebras on topologically distinct T-dual spacetimes compactified to circle bundles with HH-flux.Comment: 21 pages. 3 references added and to appear in Contemp. Mat

    Holomorphic Quillen determinant line bundles on integral compact Kahler manifolds

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    We show that any compact Kahler manifold with integral Kahler form, parametrizes a natural holomorphic family of Cauchy-Riemann operators on the Riemann sphere such that the Quillen determinant line bundle of this family is isomorphic to a sufficiently high tensor power of the holomorphic line bundle determined by the integral Kahler form. We also establish a symplectic version of the result. We conjecture that an equivariant version of our result is true.Comment: Latex2e, 10 pages, To appear in, Quillen memorial issue, Quarterly J. Mat

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

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    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.Comment: 4 pages, latex2e, Mistake in formula corrected, ref. adde

    Exotic twisted equivariant cohomology of loop spaces, twisted Bismut-Chern character and T-duality

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    We define exotic twisted S1S^1-equivariant cohomology for the loop space LZLZ of a smooth manifold ZZ via the invariant differential forms on LZLZ with coefficients in the (typically non-flat) holonomy line bundle of a gerbe, with differential an equivariantly flat superconnection. We introduce the twisted Bismut-Chern character form, a loop space refinement of the twisted Chern character form, which represent classes in the completed periodic exotic twisted S1S^1-equivariant cohomology of LZLZ. We establish a localisation theorem for the completed periodic exotic twisted S1S^1-equivariant cohomology for loop spaces and apply it to establish T-duality in a background flux in type II String Theory from a loop space perspective.Comment: 23 pages. To appear in CM

    On a generalized Connes-Hochschild-Kostant-Rosenberg theorem

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    The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalizing some fundamental results of Connes and Hochschild-Kostant-Rosenberg. The Connes-Chern character is also identified here with the twisted Chern character.Comment: 35 pages, latex2e, uses xypic. To appear in, Advances in Mathematic
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