Magnetic lattices for orthosymplectic 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.

“…In the following, we will denote SU(n)/Z k gauge groups by yellow nodes with the label n/Z k , as in (2.1). See also [50] a for a related recent discussion.…”

Section: Jhep05(2021)274mentioning

confidence: 99%

Section: Hb[t 5dmentioning

confidence: 99%

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

Closset

Giacomelli

Schäfer‐Nameki

et al. 2021

116

210

“…Instead, one must rely on other approaches, using various stringtheory dualities. A particularly fruitful approach, in recent years, has been the study of (p, q)-brane webs engineering T 5d X [29], and the related concept of a "magnetic quiver" whose 3d Coulomb branch is identical to the hyper-Kähler cone of the HB, M H [T 5d X ], that we would like to understand [27,30,31,33,34,38,102]. One interesting outcome of the present work is that it provides a derivation from the geometry of magnetic quivers for the SCFT T 5d X defined as in (1.2), at least in a number of cases [10].…”

Section: Jhep02(2021)003mentioning

confidence: 99%

Coulomb and Higgs branches from canonical singularities. Part 0

Closset

Schäfer‐Nameki

Wang

2021

155

290

Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d $$ \mathcal{N} $$ N = 4 mirror symmetry and an S-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry. As an application of the general framework, we observe that singularities that engineer Argyres-Douglas theories in Type IIB also give rise to rank-0 5d SCFTs in M-theory. We also compute the higher-form symmetries of the 4d and 5d SCFTs, including the one-form symmetries of generalized Argyres-Douglas theories of type (G, G′).

“…recent development is to use 3d N = 4 theories as a probe to study higher dimensional superconformal field theories (SCFTs) as well as gauge theories [2][3][4][5][6][7][8][9][10][11][12][13][14]. The idea is to relate the Higgs branch of these higher dimensional theories to the Coulomb branch of the 3d theory, the latter of which is dubbed magnetic quiver (MQ).…”

Section: Jhep05(2021)269mentioning

confidence: 99%

Factorised 3d $$ \mathcal{N} $$ = 4 orthosymplectic quivers

Akhond

Carta

Dwivedi

et al. 2021

We study the moduli space of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $$ \mathcal{N} $$ N = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.