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We develop an approach to the study of Coulomb branch operators in 3D $mathcal{N}=4$ 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.
The moduli space of centred Bogomolny-Prasad-Sommmerfield 2-monopole fields is a 4-dimensional manifold M with a natural metric, and the geodesics on M correspond to slow-motion monopole dynamics. The best-known case is that of monopoles on R^3, wher
In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrodinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the E
Monopole bubbling effect is screening of magnetic charges of singular Dirac monopoles by regular t Hooft-Polyakov monopoles. We study properties of weak coupling perturbative series in the presence of monopole bubbling effects as well as instantons.
We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in $4d$ $mathcal{N}=2$ superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular,
In this paper we apply the idea of Higgs branch localization to 5d supersymmetric theories of vector multiplet and hypermultiplets, obtained as the rigid limit of $mathcal{N} = 1$ supergravity with all auxiliary fields. On supersymmetric K-contact/Sa