Abstract
We propose a construction of the quantumcorrected Coulomb branch of a general 3d gauge theory with N=4 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 hyperkähler 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 the Bogomolnyi and/or Nahm equations.
Original language  English 

Pages (fromto)  671–751 
Number of pages  81 
Journal  Communications in Mathematical Physics 
Volume  354 
Issue number  2 
Early online date  3 Jun 2017 
DOIs  
Publication status  Published  30 Sep 2017 
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Tudor Dimofte
 School of Mathematics  Reader in Algebra, Geometry & Topology and related fields
Person: Academic: Research Active (Teaching)