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Journal of High Energy Physics

, 2019:26 | Cite as

Flavor symmetries and the topology of special Kähler structures at rank 1

  • Philip C. Argyres
  • Matteo LotitoEmail author
Open Access
Regular Article - Theoretical Physics
  • 9 Downloads

Abstract

We propose a method for determining the flavor charge lattice of the continuous flavor symmetry of rank-1 4d \( \mathcal{N} \) = 2 superconformal field theories (SCFTs) and IR free gauge theories from topological invariants of the special Kähler structure of the mass-deformed Coulomb branches (CBs) of the theories. The method is based on the middle homology of the total space of the elliptic fibration over the CB, and is a generalization of the F-theory string web description of flavor charge lattices. The resulting lattices, which we call “string web lattices”, contain not only information about the flavor symmetry of the SCFT but also additional information encoded in the lattice metric derived from the middle homology intersection form. This additional information clearly reflects the low energy electric and magnetic charges of BPS states on the CB, but there are other properties of the string web lattice metric which we have not been able to understand in terms of properties of the BPS spectrum. We compute the string web lattices of all rank-1 SCFTs and IR free gauge theories. We find agreement with results obtained by other methods, and find in a few cases that the string web lattice gives additional information on the flavor symmetry.

Keywords

Extended Supersymmetry Nonperturbative Effects 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) 2019

Authors and Affiliations

  1. 1.Physics DepartmentUniversity of CincinnatiCincinnatiU.S.A.
  2. 2.Amherst Center for Fundamental Interactions, Physics DepartmentUniversity of MassachusettsAmherstU.S.A.

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