Coulomb branch quantization and abelianized monopole bubbling

• Published in: The journal of high energy physics 2019-10, Vol.2019 (10), p.1-96, Article 179
• Main Authors: Dedushenko, Mykola, Fan, Yale, Pufu, Silviu S., Yacoby, Ran
• Format: Article
• Language: English
• Subjects: Algebra; Boundary conditions; Bubbling; Classical and Quantum Gravitation; Elementary Particles; Extended Supersymmetry; High energy physics; Measurement; Monopoles; Operators (mathematics); Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Solitons Monopoles and Instantons; String Theory; Supersymmetric Gauge Theory; Supersymmetry and Duality
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2019)179

A bstract We develop an approach to the study of Coulomb branch operators in 3D N = 4 gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For “good” and “ugly” theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.