Tropical geometry and five dimensional Higgs branches at infinite coupling

Cabrera, Santiago (0000 0001 2113 8111, Theoretical Physics, The Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom) ; Hanany, Amihay (0000 0001 2113 8111, Theoretical Physics, The Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom) ; Yagi, Futoshi (0000 0004 1791 7667, School of Mathematics, Southwest Jiaotong University, west zone, high-tech district, Chengdu, Sichuan, 611756, China) (0000000121102151, Department of Physics, Technion — Israel Institute of Technology, Haifa, 32000, Israel)

13 January 2019

Abstract: 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 N c for an SU N c gauge theory, number of fundamental flavors N f , 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 ( N c = 2 , N f = 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 .


Published in: JHEP 1901 (2019) 068
Published by: Springer/SISSA
DOI: 10.1007/JHEP01(2019)068
arXiv: 1810.01379
License: CC-BY-4.0



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