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The singularity structure of scale-invariant rank-2 Coulomb branches

  • Philip C. Argyres
  • Cody Long
  • Mario Martone
Open Access
Regular Article - Theoretical Physics

Abstract

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 \( \mathcal{N}=2 \) superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the U(1) R symmetry. A set of novel topological and geometric results are developed which promise to be useful for the study and classification of Coulomb branch geometries at all ranks.

Keywords

Conformal Field Theory Differential and Algebraic Geometry Extended Supersymmetry Supersymmetric Gauge Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Physics DepartmentUniversity of CincinnatiCincinnatiU.S.A.
  2. 2.Walter Burke Institute for Theoretical Physics, California Institute of TechnologyPasadenaU.S.A.
  3. 3.Department of PhysicsNortheastern UniversityBostonU.S.A.
  4. 4.Physics DepartmentUniversity of Texas, AustinAustinU.S.A.

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