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.

Highlights

  • For generic N = 1 theories it is not possible to separate distinct branches of supersymmetric vacua, the study of their moduli space is in general complicated. It has been recently understood [15,16,17,19,20] that there is a special but very broad and interesing class of N = 1 superconformal theories (SCFTs), the so called N = 1 theories of class Sk [12], for which it is possible to distinguish between generalized Coulomb and Higgs branches precisely as for N = 2 gauge theories

  • Below |ms | the singlet u2 can be integrated out and can be neglected when we deal with the low energy dynamics of gauge field [3,4,33]

  • The low energy effective theory in this limit is described by an SU (2) gauge theory with an adjoint field φ = E1 (Φ1 Φ2 − 12 tr Φ1 Φ2 ) and three singlets B1, B2 and u2

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Summary

Introduction

For generic N = 1 theories it is not possible to separate distinct branches of supersymmetric vacua, the study of their moduli space is in general complicated It has been recently understood [15,16,17,19,20] that there is a special but very broad and interesing class of N = 1 superconformal theories (SCFTs), the so called N = 1 theories of class Sk [12], for which it is possible to distinguish between generalized Coulomb and Higgs branches precisely as for N = 2 gauge theories. The construction of [3] produces the curves in a form which can be thought of as the IR form, capturing low energy data on the generalized Coulomb branch

General Principles
Examples
IR Curves of Class Sk Theories
Classical Analysis
Mass Parameters
Diagonal Limit
Checks
UV Curves of Class Sk Theories
Review of UV Curves of Class S Theories
Class Sk
Conclusions
Full Text
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