Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 354, Issue 2, Pages 671-751Publisher
SPRINGER
DOI: 10.1007/s00220-017-2903-0
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Funding
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Economic Development Innovation
- DOE [DE-SC0009988]
- ERC Starting Grant [335739]
- European Research Council under the European Union's Seventh Framework Programme
- IAS Princeton through the Martin A. and Helen Choolijan Membership
- European Research Council (ERC) [335739] Funding Source: European Research Council (ERC)
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We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on the Coulomb branch are given by expectation values of chiral monopole operators. We construct the chiral ring of such operators, using equivariant integration over BPS moduli spaces. We also quantize the chiral ring, which corresponds to placing the 3d theory in a 2d Omega background. Then, by unifying all complex structures in a twistor space, we encode the full hyperkahler metric on the Coulomb branch. We verify our proposals in a multitude of examples, including SQCD and linear quiver gauge theories, whose Coulomb branches have alternative descriptions as solutions to Bogomolnyi and/or Nahm equations.
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