Coulomb branches of 3-dimensional gauge theories and related structures

Alexander Braverman; Michael Finkelberg

Coulomb branches of 3-dimensional gauge theories and related structures

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arxiv 1807.09038 v4 pith:IECHAI5W submitted 2018-07-24 math.AG hep-thmath.RT

Alexander Braverman , Michael Finkelberg This is my paper · ORCID

classification math.AGhep-thmath.RT

keywords gaugetheoriesbranchesconstructionscoulombdiscussgeometricnotes

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These are (somewhat informal) lectures notes for the CIME summer school "Geometric Representation Theory and Gauge Theory" in June 2018. In these notes we review the results and constructions of a series of our joint papers with H.Nakajima where a mathematical definition of Coulomb branches of 3d N=4 quantum gauge theories (of cotangent type) is given. We also discuss some further constructions (such as categories of line operators in the corresponding topologically twisted theories) and briefly discuss a connection to local geometric Langlands correspondence.

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Functoriality of Coulomb branches
math.AG 2025-01 conditional novelty 7.0 of 10

Gluable maps of reductive groups make Coulomb branches compose via Hamiltonian reduction, yielding a proof that T^*(G/U_P) for GL_n and SL_n is a Coulomb branch.

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