Related papers: Exceptional Algebra and Sporadic Groups at c=12
Enhancement of global symmetry and supersymmetry in the infrared is one of the most intriguing phenomena in quantum field theory. We investigate such phenomena in a large class of three dimensional superconformal field theories, known as…
We present a new construction of four dimensional $\mathcal N=3$ theories, given by M5 branes wrapping a $T^2$ in an M-theory U-fold background. The resulting setup generalizes the one used in the usual class $\mathcal S$ construction of…
We classify the class $S$ theories of type $E_7$. These are four-dimensional $\mathcal{N}=2$ superconformal field theories arising from the compactification of the $E_7$ $(2,0)$ theory on a punctured Riemann surface, $C$. The classification…
We generate by computer a basis of invariants for the fundamental representations of the exceptional Lie groups E(6) and E(7), up to degree 18. We discuss the relevance of this calculation for the study of supersymmetric gauge theories, and…
We study the interplay between holomorphic conformal field theory and dualities of 3D topological quantum field theories generalizing the paradigm of level-rank duality. A holomorphic conformal field theory with a Kac-Moody subalgebra…
Superconformal field theories (SCFT) are known to possess solvable yet nontrivial sectors in their full operator algebras. Two prime examples are the chiral algebra sector on a two dimensional plane in four dimensional $\mathcal{N}=2$…
As is well-known, the compact groups Spin(7) and SO(7) both have a single conjugacy class of compact subgroups of exceptional type G_2. We first show that if H is a subgroup of Spin(7), and if each element of H is conjugate to some element…
Superconformal symmetry in six-dimensions is analyzed in terms of coordinate transformations on superspace. A superconformal Killing equation is derived and its solutions are identified in terms of supertranslations, dilations, Lorentz…
We study chiral algebras in the $\bar{Q}$-cohomology of two dimensional SYK models with extended supersymmetry. In a special limit discovered in arXiv:1805.09325, we are able to construct explicitly a "vertical" single-particle higher-spin…
Chiral orbifold models are defined as gauge field theories with a finite gauge group $\Gamma$. We start with a conformal current algebra A associated with a connected compact Lie group G and a negative definite integral invariant bilinear…
We study a self-dual N=1 super vertex operator algebra and prove that the full symmetry group is Conway's largest sporadic simple group. We verify a uniqueness result which is analogous to that conjectured to characterize the Moonshine…
We prove versions of super spin-charge separation for all three of the symmetry groups SU(N), Sp(2N), and SO(N) of disordered Dirac fermions in 2+1 dimensions, which involve the supercurrent-algebras gl (1|1)_{N}, osp(2|2)_{-2N}, and…
In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1 $\mathcal{N}=2$ SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 $\mathcal{N}=2$…
We recall Schur's work on universal central extensions and develop the analogous theory for categorical extensions of groups. We prove that the String 2-groups are universal in this sense and study in detail their restrictions to the finite…
Superconformal indices (SCIs) of 4d ${\mathcal N}=4$ SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For $F_4, E_6, E_7, E_8$ gauge groups this yields first examples of integrals of such…
Every six-dimensional $\mathcal{N}=(2,0)$ SCFT on $\mathbf{R}^6$ contains a set of protected operators whose correlation functions are controlled by a two-dimensional chiral algebra. We provide an alternative construction of this chiral…
We present a novel approach to classify supersymmetric effective field theories (EFTs) whose scattering amplitudes exhibit enhanced soft limits. These enhancements arise due to non-linearly realised symmetries on the Goldstone modes of such…
We study realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine symmetry currents, respectively. Both the N=8 and N=7 algebras admit unitary…
Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz…
The realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine symmetry currents are reviewed. Both the N=8 and N=7 algebras admit unitary realizations in…