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

Abstract

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.

Conformal manifolds and 3d mirrors of Argyres-Douglas theories

“…Contrary to D b p (SU(N )) theories, whose reduction to 3d always leads to a Lagrangian theory [22,23], we do not have such a description for the class of theories studied in the present paper. As a result, the quiver description of each mirror theory in this paper is obtained by guesswork, based on information about the CB dimension, the value of JHEP08(2021)015 24(c − a) and the number of mass parameters of the original 4d theory in question.…”

“…1 In the same way as in [22], we refer to such a sector as the non-Higgsable SCFTs. These theories dimensionally reduce to free twisted hypermultiplets [22][23][24], which then correspond to the free hypermultiplets sector under the mirror map.…”

“…free hypermultiplets, together with a quiver gauge theory that can be constructed as follows: 23 1. Construct a complete graph with m SO(2) nodes such that every edge has multiplicity…”

“…The logic for this is the following. The magnetic quiver of a 4d theory engineered by IIB on a given CY X is related to the electric quiver of the 5d theory engineered by Atheory on the same CY X by an operation consisting in gauging the topological symmetry (see figure 1 in [23]). However, the mirrors we consider here are just free hypers, so there is no topological symmetry that can be gauged.…”

Higgs branches of 5d rank-zero theories from geometry

“…In the past five years, the subject has seen a revival, with more thorough systematic studies of such theories, their global symmetries, their moduli spaces, their prepotentials, and various methods for constructing them. It is difficult at this point to reference all works, some key works include [6][7][8][9][10][11][12][13][14][15]. From that perspective, the Higgs branch will be realized by the complex structure moduli and the Wilson lines of the supergravity C 3 -form.…”