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Beyond the string genus. (English) Zbl 1229.81212

Summary: In an earlier work we used a path integral analysis to propose a higher genus generalization of the elliptic genus. We found a cobordism invariant parametrized by Teichmuller space. Here we simplify the formula and study the behavior of our invariant under the action of the mapping class group of the Riemann surface. We find that our invariant is a modular function with multiplier just as in genus one.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
57R57 Applications of global analysis to structures on manifolds
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References:

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