Dynamics Of 3D Coulomb Branches
In this thesis we focus on the dynamics of Coulomb branches in 3 dimensional N = 2 SUSY theories. The first part of this thesis is dedicated for the most part to a review of previously known results, providing the necessary background to understand the generalization to more complicated theories. We review in details both the behavior of U(1) theories with generic number of flavors and S U(N) theories with fundamentals. We also provide insights on the mapping of Coulomb branch operators across dualities as vortex/monopole operators. In the second part of the thesis we investigate the IR dynamics of N = 2 SUSY gauge theories in 3D with antisymmetric matter. The presence of the antisymmetric fields leads to further splitting of the Coulomb branch. Counting zero modes in the instanton background suggests that more than a single direction along the Coulomb branch may remain unlifted. We examine the case of S U(4) with one or two antisymmetric fields and various flavors in detail. Using the results for the corresponding 4D theories, we find the IR dynamics of the 3D cases via compactification and a real mass deformation. We find that for the s-confining case with two antisymmetric fields, a second unlifted Coulomb branch direction indeed appears in the lowenergy dynamics. We present several non-trivial consistency checks to establish the validity of these results. We also comment on the expected structure of general s-confining theories in 3D, which might involve several unlifted Coulomb branch directions. The original work presented in this thesis is mostly based on . The paper will appear soon on JHEP.
McAllister, Liam; Thom-Levy, Julia
Ph.D. of Physics
Doctor of Philosophy
dissertation or thesis