Classes on the moduli space of Riemann surfaces through a noncommutative Batalin-Vilkovisky formalism

Details Classes on the moduli space of Riemann surfaces through a noncommutative Batalin-Vilkovisky formalism Classes on the moduli space of Riemann surfaces through a noncommutative Batalin-Vilkovisky formalism

2011-04-22

arxiv.org/abs/1104.4372v1

Mathematics

Quantum Algebra

27 pages, 4 figures

Scientific paper

Using the machinery of the Batalin-Vilkovisky formalism, we construct cohomology classes on compactifications of the moduli space of Riemann surfaces from the data of a contractible differential graded Frobenius algebra. We describe how evaluating these cohomology classes upon a well-known construction producing homology classes in the moduli space can be expressed in terms of the Feynman diagram expansion of some functional integral. By computing these integrals for specific examples, we are able to demonstrate that this construction produces families of nontrivial classes.

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