Fibrations and Hasse diagrams for 6d SCFTs

Abstract

We study the full moduli space of vacua of 6d worldvolume SCFTs on M5 branes probing an A-type singularity, focusing on the geometric incarnation of the discrete gauging mechanism which acts as a discrete quotient on the Higgs branch fibered over the tensor branch. We combine insights from brane constructions and magnetic quiver techniques, in which discrete gauging is implemented through the concept of decoration introduced in [1]. We discover and characterize new transverse slices between phases of 6d SCFTs, identifying some of them with a family of isolated symplectic singularities recently discovered in [2], and conjecturing the existence of two new isolated symplectic singularities.

Actions on the quiver: discrete quotients on the Coulomb branch

“…5 64 bouquet is introduced and discussed in [36,37]. The investigation of the decorated quiver with a non-simply-laced bouquet or complete graphs is left for future work.…”

A new family of isolated symplectic singularities with trivial local fundamental group

“…Proof of (6.2). By definition, ℂ[(𝑑)]∕⟨𝔪⟩ is the commutative ℂ-algebra whose presentation is given by It was recently observed in [11] that this is the Hilbert for the Coulomb branch singularity associated to a certain 6-dimensional superconformal field theory [11, A.1]. It is conjectured that these singularities are equivalent.…”

The Geometry of Quivers

“…Conversely, even within the realm of Higgs branches one can go much beyond Nakajima quiver varieties, as we saw in Section 2.3. It turns out one can often still find magnetic quivers for these Higgs branches [28][29][30][31][32][33][34], thus opening a window into the geometry of the moduli space, and various deductions about deformations and the renormalization group flow. Another subtlety arises when the Higgs branch is not an irreducible variety.…”