Tropical geometry and five dimensional Higgs branches at infinite coupling

  • Santiago Cabrera
  • Amihay Hanany
  • Futoshi YagiEmail author
Open Access
Regular Article - Theoretical Physics


Superconformal five dimensional theories have a rich structure of phases and brane webs play a crucial role in studying their properties. This paper is devoted to the study of a three parameter family of SQCD theories, given by the number of colors Nc for an SU Nc gauge theory, number of fundamental flavors Nf, and the Chern Simons level k. The study of their infinite coupling Higgs branch is a long standing problem and reveals a rich pattern of moduli spaces, depending on the 3 values in a critical way. For a generic choice of the parameters we find a surprising number of 3 different components, with intersections that are closures of height 2 nilpotent orbits of the flavor symmetry. This is in contrast to previous studies where except for one case (Nc = 2, Nf = 2), the parameters were restricted to the cases of Higgs branches that have only one component. The new feature is achieved thanks to a concept in tropical geometry which is called stable intersection and allows for a computation of the Higgs branch to almost all the cases which were previously unknown for this three parameter family apart form certain small number of exceptional theories with low rank gauge group. A crucial feature in the construction of the Higgs branch is the notion of dressed monopole operators.


Brane Dynamics in Gauge Theories Field Theories in Higher Dimensions Supersymmetric Gauge Theory 


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.Theoretical Physics, The Blackett LaboratoryImperial College LondonLondonUnited Kingdom
  2. 2.School of MathematicsSouthwest Jiaotong UniversityChengduChina
  3. 3.Department of Physics, Technion — Israel Institute of TechnologyHaifaIsrael

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