Archimedean L-factors and Topological Field Theories I

Details Archimedean L-factors and Topological Field Theories I Archimedean L-factors and Topological Field Theories I

2009-06-05

arxiv.org/abs/0906.1065v2

Mathematics

Number Theory

31 pages, typos corrected

Scientific paper

We propose a functional integral representation for Archimedean L-factors given by products of Gamma-functions. The corresponding functional integral arises in the description of type A equivariant topological linear sigma model on a disk. The functional integral representation provides in particular an interpretation of the Gamma-function as an equivariant symplectic volume of an infinite-dimensional space of holomorphic maps of the disk to C. This should be considered as a mirror-dual to the classical Euler integral representation of the Gamma-function. We give an analogous functional integral representation of q-deformed Gamma-functions using a three-dimensional equivariant topological linear sigma model on a handlebody. In general, upon proper ultra-violent completion, the topological sigma model considered on a particular class of three-dimensional spaces with a compact Kahler target space provides a quantum field theory description of a K-theory version of Gromov-Witten invariants.

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