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From S-duality to Quantum Cohomology
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Abstract:
We compute quantum cohomology rings of target manifolds of a large family of 3d (2,2) sigma models using integrability. As a first step we use the Nekrasov-Shatashvili duality between the chiral ring and the space of solutions of the corresponding integrable spin chain. Second, we construct a dual classical integrable system to the spin chain whose phase space is identified with the parameter space of mass deformations of the 3d theory. On the final step integrability is used to relate the conserved charges of the latter integrable system with relations of the quantum cohomology ring. Our construction generalizes the results by Givental, Kim, Rujsenaars and others. We discuss quantization of the classical integrable system involved in our construction.
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