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Twisted differential String and Fivebrane structures
, 2009
"... Abelian differential generalized cohomology as developed by Hopkins and Singer has been shown by Freed to formalize the global description of anomaly cancellation problems in String theory, such as notably the GreenSchwarz mechanism. On the other hand, this mechanism, as well as the FreedWitten an ..."
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Cited by 26 (21 self)
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Abelian differential generalized cohomology as developed by Hopkins and Singer has been shown by Freed to formalize the global description of anomaly cancellation problems in String theory, such as notably the GreenSchwarz mechanism. On the other hand, this mechanism, as well as the FreedWitten anomaly cancellation, are fundamentally governed by the cohomology classes represented by the relevant nonabelian O(n) and U(n)principal bundles underlying the tangent and the gauge bundle on target space. In this article we unify the picture by describing nonabelian differential cohomology and twisted nonabelian differential cohomology and apply it to these situations. We demonstrate that the FreedWitten mechanism for the Bfield, the GreenSchwarz mechanism for the H3field, as well as its magnetic dual version for the H7field define cocycles in twisted nonabelian differential cohomology that may be addressed, respectively, as twisted Spin(n), twisted String(n) and twisted Fivebrane(n)structures on target space, where the twist in each case is provided by the obstruction to lifting the gauge bundle through a higher connected cover of U(n). We work out the (nonabelian) L∞algebra valued connection data provided by the differential refinements of these twisted cocycles and demonstrate that this reproduces locally the differential form data with the twisted Bianchi identities as known from the
Frobenius map for quintic threefolds
"... Abstract. We calculate the matrix of the Frobenius map on the middle dimensional cohomology of the one parameter family that is related by mirror symmetry to the family of all quintic threefolds. 1. ..."
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Cited by 4 (1 self)
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Abstract. We calculate the matrix of the Frobenius map on the middle dimensional cohomology of the one parameter family that is related by mirror symmetry to the family of all quintic threefolds. 1.
FROBENIUS MAP ON LOCAL CALABIYAU MANIFOLDS
, 810
"... Abstract. We prove results that, for a certain class of noncompact CalabiYau threefolds, relate the Frobenius action on their padic cohomology to the Frobenius action on the padic cohomology of the corresponding curves. In the appendix, we describe our interpretation of the GriffithsDwork metho ..."
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Abstract. We prove results that, for a certain class of noncompact CalabiYau threefolds, relate the Frobenius action on their padic cohomology to the Frobenius action on the padic cohomology of the corresponding curves. In the appendix, we describe our interpretation of the GriffithsDwork method. 1.