Abstract

Magnetic quivers have led to significant progress in the understanding of gauge theories with 8 supercharges at UV fixed points. For a given low-energy gauge theory realised via a Type II brane construction, there exist magnetic quivers for the Higgs branches at finite and infinite gauge coupling. Comparing these moduli spaces allows one to study the non-perturbative effects when transitioning to the fixed point. For 5d mathcal{N} = 1 SQCD, 5-brane webs have been an important tool for deriving magnetic quivers. In this work, the emphasis is placed on 5-brane webs with orientifold 5-planes which give rise to 5d theories with orthogonal or symplectic gauge groups. For this set-up, the magnetic quiver prescription is derived and contrasted against a unitary magnetic quiver description extracted from an O7− construction. Further validation is achieved by a derivation of the associated Hasse diagrams. An important class of families considered are the orthogonal exceptional En families (−∞ < n ≤ 8), realised as infinite coupling Higgs branches of Sp(k) gauge theories with fundamental matter. In particular, the moduli spaces are realised by a novel type of magnetic quivers, called unitary-orthosymplectic quivers.

Highlights

  • 5-dimensional N =1 gauge theories are perturbatively non-renormalisable and can only meaningfully be defined as mass deformations of renormalisation group fixed points

  • The Higgs branches of 5d N = 1 theories with symplectic or orthogonal gauge groups and fundamental matter are investigated at finite and infinite gauge coupling

  • Based on the 5-brane web realisations in the presence of O5 orientifold planes, the key technique for this study is the use of magnetic quivers

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Summary

Introduction

5-dimensional N =1 gauge theories are perturbatively non-renormalisable and can only meaningfully be defined as mass deformations of renormalisation group fixed points. Moving on to the infinite coupling Higgs branches, the enhancement of the global symmetry has been studied via field theory [35] and brane webs [9]. Dimension and global symmetry of H∞ are known, but no geometrical description has been provided yet This is precisely the first aim of the present paper: to provide an improved description of finite and infinite coupling Higgs branches. Concerning orthogonal or symplectic gauge theories without complete Higgsing, the magnetic quivers provide predictions on the finite and infinite coupling Higgs branches. Having derived the magnetic quivers for finite and infinite coupling Higgs branch in a variety of cases, section 5 details the derivation of the associated Hasse diagrams. +νμ2k+4(tk+1 +tk+3)+μ22k+4t2k+4 −ν2μ22k+4t2k+6 k μ2it2i i=1 k μ2it2i +t2 +(μ2k+2q +μ2k+3q−1)tk+1 i=1 k μ2it2i +t2 +(q +q−1)μ2k+2tk+1 i=1

Set-up
Magnetic quivers
E0 theory
Rules for magnetic quivers
Infinite coupling
Finite coupling
Duality with 5d SQCD
Two realisations
Problem of two cones
Hasse diagrams and quiver subtraction
E8 family
E7 family
E6 family
E5 family
E4 family
E3 family
E2 family
E1 family
Conclusion
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