Abstract
With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class {mathcal{S}}_{varGamma } . The class {mathcal{S}}_{varGamma } theories arise from M5-branes probing ℂ2/Γ, an ADE singularity. The resulting 4D theories descend from compactification on Riemann surfaces decorated with punctures. We show that for class {mathcal{S}}_{varGamma } theories, a puncture is specified by singular boundary conditions for fields in the 5D quiver gauge theory obtained from compactification of the 6D theory on a cylinder geometry. We determine general boundary conditions and study in detail solutions with first order poles. This yields a generalization of the Nahm pole data present for 1/2 BPS punctures for theories of class mathcal{S} . Focusing on specific algebraic structures, we show how the standard discussion of nilpotent orbits and its connection to representations of mathfrak{s}mathfrak{u}(2) generalizes in this broader context.
Highlights
N = 2 supersymmetric systems that have been studied extensively [6]
We show that for class SΓ theories, a puncture is specified by singular boundary conditions for fields in the 5D quiver gauge theory obtained from compactification of the 6D theory on a cylinder geometry
In this paper we have given a general characterization of 1/2 BPS regular punctures of (1, 0) SCFTs defined by a stack of M5branes probing an ADE singularity: class SΓ theories
Summary
We introduce the primary class of theories for which we will study punctures. An equivalent method is to treat the higher-dimensional theory in terms of a collection of 4D fields in which we only impose the standard supersymmetric equations of motion for the 4D theory This will lead us to boundary conditions which preserve four real supercharges. Since we are interested in possible boundary conditions which preserve a 4D Lorentz invariant vacuum with N = 1 supersymmetry, much as in reference [40], it is helpful to assemble the mode content of this 5D theory in terms of a collection of N = 1 multiplets parameterized by points of the factor R of the cylinder S1×R With this in mind, we have a collection of 4D vector multiplets, and three adjoint-valued chiral multiplets, all of which are labelled by internal points of R.
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