Abstract
We compute the exact two-sphere partition function and matrix of two-point functions of operators in the chiral ring with their complex conjugates in two-dimensional supersymmetric gauge theories. For gauge theories that flow in the infrared to a Calabi-Yau nonlinear sigma model, these renormalization group invariant observables determine the exact Kahler potential and associated Zamolodchikov metric in the complex structure moduli space of the Calabi-Yau manifold.
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