3d Coulomb branch and 5d Higgs branch at infinite coupling

Abstract

The Higgs branch of minimally supersymmetric five dimensional SQCD theories increases in a significant way at the UV fixed point when the inverse gauge coupling is tuned to zero. It has been a long standing problem to figure out how, and to find an exact description of this Higgs branch. This paper solves this problem in an elegant way by proposing that the Coulomb branches of three dimensional N = 4 supersymmetric quiver gauge theories, named "Exceptional Sequences", provide the solution to the problem. Thus, once again, 3d N = 4 Coulomb branches prove to be useful tools in solving problems in higher dimensions. Gauge invariant operators on the 5d side consist of classical objects such as mesons, baryons and gaugino bilinears, and non perturbative objects such as instanton operators with or without baryon number. On the 3d side we have classical objects such as Casimir invariants and non perturbative objects such as monopole operators, bare or dressed. The duality map works in a very interesting way.

D-type conformal matter and SU/USp quivers

“…It is interesting to study the BPS spectrum, particularly the Higgs branch chiral ring, of this theory as this can teach us about the operator spectrum of the original 6d SCFT. In our case, a detailed analysis of the Higgs branch was performed in [26] primarily using the 3d mirror quiver one gets when compactifying the 5d SCFT to 3d. We next review some aspects of this analysis while referring the reader interested in more in depth study of the Higgs branch to the reference.…”

Discrete gauging in six dimensions

“…4 For these cases we can use the results of [25], which give a prescription for the 3d quiver in terms of 6d data like the associated lowenergy quiver semi-gauge theory on a generic point on the tensor branch. The prescription is rather involved so we refer the interested reader to the reference for details.…”

“…The approach taken in a recent set of papers [3][4][5], and in the present paper, is to study the behavior of the Higgs branch as one tunes a gauge coupling to infinity, or in 4 dimensions on an Argyres Douglas point at finite coupling [6]. Such an approach turns out to be particularly useful in revealing new physics related to instanton operators [3,4], small E 8 instanton transitions [7], Kraft -Procesi (KP) transitions [8][9][10] and the physics of a single M5 brane on a D type singularity [5].…”

“…Such an approach turns out to be particularly useful in revealing new physics related to instanton operators [3,4], small E 8 instanton transitions [7], Kraft -Procesi (KP) transitions [8][9][10] and the physics of a single M5 brane on a D type singularity [5]. A key feature in this approach is to express the Higgs branch at infinite coupling as a Coulomb branch of a 3d N = 4 quiver gauge theory.…”

Magnetic quivers, Higgs branches, and 6d $$ \mathcal{N} $$ = (1, 0) theories — orthogonal and symplectic gauge groups

“…More generally, Higgs branches of theories with 8 supercharges can be enlarged at the UV fixed point due to massless BPSobjects, and the classical hyper-Kähler description breaks down. For instance, Coulomb branches have already been employed successfully to describe Higgs branches of Argyres-Douglas theories [18], as well as infinite coupling limits of 5-dimensional theories [19][20][21] and of 6-dimensional gauge theories [17,[22][23][24]. In fact, by interpreting these moduli spaces as symplectic singularities [25], the magnetic quiver techniques allowed to derive the Hasse diagrams for the various Higgs branches [26].…”