Related papers: Current Algebra Levels in the $E_8$ Theory

This is a full revised version of the previous same titled article. The 2-cocycle of the central extension of the current algebra on the three sphere is taken the place of a new quarternion valued one, that is defined by the boundary Dirac…

We study theories of type $D_4$ in class-S, with nonabelian outer-automorphism twists around various cycles of the punctured Riemann surface $C$. We propose an extension of previous formul\ae\ for the superconformal index to cover this case…

We analyze the N=2 superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we…

We study a specific type of atomic Higgsings of the 6d $\mathcal{N}=(1,0)$ theories, which we call the induced flows. For the conformal matter theory associated with a pair of nilpotent orbits, the induced flows are given by the inductions…

In this paper we begin mapping out the space of rank-2 $\mathcal{N}=2$ superconformal field theories (SCFTs) in four dimensions. This represents an ideal set of theories which can be potentially classified using purely quantum…

The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one theories with $E_n$ flavour symmetry. We study their $U$-plane, which is the one-dimensional Coulomb branch of the theory on $\mathbb{R}^4 \times S^1$.…

We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra $\mathfrak g$. We analyse classes of quiver theories, with Classical gauge and flavour…

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…

We extend the Mellin space techniques of [1] for computing holographic four-point correlation functions in maximally superconformal theories to theories with only eight Poincar\'e supercharges. The one-half BPS operators in these…

We generalize recent construction of four-dimensional $\mathcal{N}=1$ SCFT from wrapping six-dimensional $\mathcal{N}=(2,0)$ theory on a Riemann surface to the case of $D$-type with outer-automorphism twists. This construction allows us to…

We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory…

Extending the scalar sector helps in studying the Higgs mechanism and some Standard Model problems. We implement the correspondence between the gauge-dependent elementary states and the non-perturbative non-abelian gauge-invariant…

We study the Higgs branch and associated vertex operator algebra (VOA) of 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) from the geometric engineering of IIB superstring on canonical threefold singularities. For terminal…

We show that symmetries and gauge symmetries of a large class of 2-dimensional sigma models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the sigma…

We consider a certain ${\cal N}=1$ supersymmetric, $SO(3)\times SO(3)$ invariant, subsector of the $\omega$-deformed family of $SO(8)$-gauged ${\cal N}=8$ four-dimensional supergravities. The theory contains two scalar fields and two…

Twisted current algebras are fixed point subalgebras of current algebras under a finite group action. Special cases include equivariant map algebras and twisted forms of current algebras. Their finite-dimensional simple modules fall into…

We extend the investigation of the recently introduced class ${\cal S}_k$ of 4d $\mathcal{N}=1$ SCFTs, by considering a large family of quiver gauge theories within it, which we denote $\mathcal{S}^1_k$. These theories admit a realization…

We apply results from the geometry of nilpotent orbits and nilpotent Slodowy slices, together with modularity and asymptotic analysis of characters, to prove many new isomorphisms between affine W-algebras and affine Kac-Moody vertex…

We provide a general classification of template operators, up to next-to-leading order, that appear in chiral perturbation theories based on the two flavour patterns of spontaneous symmetry breaking SU($N_F$)/Sp($N_F$) and…

We refine our previous proposal for systematically classifying 4d rank-1 $\mathcal N=2$ SCFTs by constructing their possible Coulomb branch geometries. Four new recently discussed rank-1 theories, including novel $\mathcal{N}=3$ SCFTs, sit…