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Applying advances in exact computations of supersymmetric gauge theories, westudy the structure of correlation functions in two-dimensional N=(2,2) Abelianand non-Abelian gauge theories. We determine universal relations amongcorrelation functions, which yield differential equations governing thedependence of the gauge theory ground state on the Fayet-Iliopoulos parametersof the gauge theory. For gauge theories with a non-trivial infrared N=(2,2)superconformal fixed point, these differential equations become thePicard-Fuchs operators governing the moduli-dependent vacuum ground state in aHilbert space interpretation. For gauge theories with geometric target spaces,a quadratic expression in the Givental I-function generates the analyzedcorrelators. This gives a geometric interpretation for the correlators, theirrelations, and the differential equations. For classes of Calabi-Yau targetspaces, such as threefolds with up to two Kahler moduli and fourfolds with asingle Kahler modulus, we give general and universally applicable expressionsfor Picard-Fuchs operators in terms of correlators. We illustrate our resultswith representative examples of two-dimensional N=(2,2) gauge theories.

The Geometry of Gauged Linear Sigma Model Correlation Functions