Higher symmetries of 5D orbifold SCFTs

Abstract

We determine the higher symmetries of 5D SCFTs engineered from M-theory on a C 3 =Γ background for Γ a finite subgroup of SUð3Þ. This resolves a longstanding question as to how to extract this data when the resulting singularity is nontoric (when Γ is non-Abelian) and/or not isolated (when the action of Γ has fixed loci). The Bogomol'nyi-Prasad-Sommerfield (BPS) states of the theory are encoded in a 1D quiver quantum mechanics gauge theory which determines the possible 1-form and 2-form symmetries. We also show that this same data can also be extracted by a direct computation of the corresponding defect group associated with the orbifold singularity. Both methods agree, and these computations do not rely on the existence of a resolution of the singularity. We also observe that when the geometry faithfully captures the global 0-form symmetry, the abelianization of Γ detects a 2-group structure (when present). As such, this establishes that all of this data is indeed intrinsic to the superconformal fixed point rather than being an emergent property of an IR gauge theory phase.

On non-supersymmetric fixed points in five dimensions

“…In particular, a whole zoo of superconformal field theories (SCFT) have been shown to exist in five dimensions, some of which corresponding to possible UV completions of supersymmetric gauge theories. These conformal theories enjoy many interesting properties, such as enhancement of global symmetries [1,2,16,[47][48][49][50][51][52] and emergence of non-perturbative Higgs branches [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68].…”

McKay quivers and decomposition

“…3. In a similar vein, in the context of geometric engineering McKay quivers provide a tool to study the BPS states of certain 4d N = 2 SQFT through intepretting them as BPS quivers [37,46]. It therefore encodes properties of fractional branes, which in the context of algebraic geometry are described as coherent sheaves on a certain variety.…”

“…This information was leveraged to understand the matter content of theories descending from string theory compactified on [X/G] [15, 16,26]. More recently, for finite subgroups of SU(3), these quivers have been interpreted as 5d BPS quivers for theories coming from M-theory compactified on [C 3 /G] [37,46].…”

2-Group symmetries and M-theory

“…Since the generic supersymmetric QFT does not admit a conventional Lagrangian description, it is paramount to develop tools in string theory to detect and study the features of such generalized symmetries in the context of various geometric engineering scenarios . 3 Indeed, 2-groups structures have been computed in the literature from geometries engineering SCFTs and LSTs in various dimensions [20,21,32,43,48]. Although so far the cases of interest to us have only been studied on a resolved phase of the geometry, it seems natural to expect that 2-groups should be an intrinsic feature of these setups, encoded in the geometry of the singularity itself and not only in specific properties of its resolutions, rulings, or deformations.…”