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Generalized Witten Genus and Vanishing Theorems

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arxiv 1003.2325 v1 pith:OSZXQ7MZ submitted 2010-03-11 math.DG math.AT

Qingtao Chen , Fei Han , Weiping Zhang This is my paper · ORCID
classification math.DGmath.AT
keywords genuswittengeneralizedmanifoldsspinstringconstructtheorems
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abstract

We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin$^c$ manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of the Witten genus for $8k+2$ dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalized Witten genus and the mod 2 Witten genus on string$^c$ and string (generalized) complete intersections in (product of) complex projective spaces respectively.

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  1. Six-dimensional gauge theories and (twisted) generalized cohomology

    hep-th 2019-08 conditional novelty 6.0 of 10

    Combining an abelianized Yang-Mills field with its dual in 6D N=(1,0) supergravity yields a class in twisted K-theory, with the B-field as twist.

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