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

geometry.

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PIRSA Number:

13040141