  In the first part of this series of papers we propose a functional integral
representation for local Archimedean L-factors given by products of the
Gamma-functions. In particular we derive a representation of the Gamma-function
as a properly regularized equivariant symplectic volume of an
infinite-dimensional space. The corresponding functional integral arises in the
description of a type A equivariant topological linear sigma model on a disk.
In this paper we provide a functional integral representation of the
Archimedean L-factors in terms of a type B topological sigma model on a disk.
This representation leads naturally to the classical Euler integral
representation of the Gamma-functions. These two integral representations of
L-factors in terms of A and B topological sigma models are related by a mirror
map. The mirror symmetry in our setting should be considered as a local
Archimedean Langlands correspondence between two constructions of local
Archimedean L-factors.
