Minimally unbalanced quivers

116

210

Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d $$ \mathcal{N} $$ N = 2 SCFTs that we call $$ {D}_p^b $$ D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d $$ \mathcal{N} $$ N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class $$ \mathcal{S} $$ S realization. We also discover new S-dualities between different $$ {D}_p^b $$ D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT.

“…Its Higgs branch, as determined from the MQ (5) , is the next-to-minimal nilpotent orbit of e 8 [104]. The MQ (5) of model (3) appeared before in [105].…”

Section: Case (B α ) = (N N N )mentioning

confidence: 99%

5d and 4d SCFTs: canonical singularities, trinions and S-dualities

Closset

Giacomelli

Schäfer‐Nameki

et al. 2021

116

210

“…The global symmetry for this theory is C 5 , the dimension of the Higgs branch is 16, and there is a generator of the chiral ring at [00001] C 5 and scaling dimension 3/2. These facts lead to a guess for a magnetic quiver among the minimally unbalanced quivers of [48], where the unbalanced node is attached to the last node. We recall that for a (not necessarily simply laced) unitary quiver, the imbalance e of a given node is defined as the number of hypers attached to that node, minus twice the rank of the gauge group.…”

Section: Rank 1 Scftmentioning

confidence: 99%

Magnetic quivers for rank 1 theories

Bourget

Grimminger

Hanany

et al. 2020

Self Cite

“…We know that the global symmetry is Sp(5), hence (assuming there exists a unitary magnetic quiver) the magnetic quiver describing the Higgs branch has to be minimally unbalanced C-type. Minimally unbalanced quivers are classified in [50]. We are also provided with the dimension of the Higgs branch which is dim H (H) = 16, the only option for the magnetic quiver is:…”

Section: A C N Flavour Theorymentioning

confidence: 99%

Hasse diagrams for 3d $$ \mathcal{N} $$ = 4 quiver gauge theories — Inversion and the full moduli space

Grimminger

Hanany

2020

Self Cite

We study Hasse diagrams of moduli spaces of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories. The goal of this work is twofold: 1) We introduce the notion of inverting a Hasse diagram and conjecture that the Coulomb branch and Higgs branch Hasse diagrams of certain theories are related through this operation. 2) We introduce a Hasse diagram to map out the entire moduli space of the theory, including the Coulomb, Higgs and mixed branches. For theories whose Higgs and Coulomb branch Hasse diagrams are related by inversion it is straight forward to generate the Hasse diagram of the entire moduli space. We apply inversion of the Higgs branch Hasse diagram in order to obtain the Coulomb branch Hasse diagram for bad theories and obtain results consistent with the literature. For theories whose Higgs and Coulomb branch Hasse diagrams are not related by inversion it is nevertheless possible to produce the Hasse diagram of the full moduli space using different methods. We give examples for Hasse diagrams of the entire moduli space of theories with enhanced Coulomb branches.