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Gromov-Witten Invariants from 2D Gauge Theories

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It has been known for twenty years that a class of
two-dimensional gauge theories are intimately connected to toric geometry, as
well as to hypersurfaces or complete intersections in a toric varieties, and to
generalizations thereof.  Under renormalization
group flow, the two-dimensional gauge theory flows to a conformal field theory
that describes string propagation on the associated geometry.  This provides a connection between certain
quantities in the gauge theory and topological invariants of the associated
geometry.  In this talk, I will explain
how recent results show that, for Calabi-Yau geometries, the partition function
for each gauge theory computes the Kahler potential on the Kahler moduli of the
associated geometry.  The result is expressed
in terms of a Barnes' integral and is readily evaluated in a series expansion
around special points in the moduli space (e.g., large volume), providing a
fairly efficient way to compute Gromov-Witten invariants of the associated