𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories

Abstract

We study the low energy effective dynamics of four-dimensional N=1 superconformal theories on their generalized Coulomb branch. The low energy effective gauge couplings are naturally encoded in algebraic curves X, which we derive for general values of the couplings and mass deformations. We then recast these IR curves X to the UV or M-theory form C: the punctured Riemann surfaces on which the M5 branes are compactified giving the four-dimensional theories. We find that the UV curves C and their corresponding meromorphic differentials take the same form as those for their mother four-dimensional N=2 theories of class S. They have the same poles, and their residues are functions of all the exactly marginal couplings and the bare mass parameters which we can compute exactly.

Instanton counting in class Sk

“…However, it is not any more clear what the precise physical interpretation of the a parameters is. We are currently tying to understand this point [105], by backing up, deriving and studying the SW curves away from the orbifold point, following the work of [106].…”

“…At this stage it is unclear to us if this is even possible, however we believe that carefully studying the SW curves away from the orbifold point [105] will be illuminating. A comment concerning our strategy is in order.…”

Aspects of 4d supersymmetric dynamics and geometry

“…70 See [229] discussing all three approaches. 71 This approach can be applied in certain cases also for N = 1 theories [236], which was studied for theories obtained from M5 branes on A type orbifolds in [237][238][239][240][241].…”