Archimedean $L$-factors and topological field theories I
Anton A. Gerasimov, Dimitri Lebedev, Sergey Oblezin · Communications in Number Theory and Physics · 2011
We propose a functional integral representation for Archimedean L-factors given by products of Γ-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 Γ-function as an equivariant symplectic volume of an infinitedimensional 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 Γ-function.We give an analogous functional integral representation of q-deformed Γ-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 threedimensional spaces with a compact Kähler target space provides a quantum field theory description of a K-theory version of Gromov-Witten invariants.