Related papers: Exceptional Algebra and Sporadic Groups at c=12
Exploiting the symmetry topological field theory/topological order correspondence (SymTFT/TO), together with the higher-categorical structure of 6D N =(2,0) SCFTs, we prove that the total quantum dimension of the relative gaugeable algebra…
We consider the 6d (1,0) SCFT on a stack of $N$ M5-branes probing a $\mathbb C^2/\mathbb Z_2$ singularity. In particular, we study its compactifications to four dimensions on a smooth genus-$g$ Riemann surface with non-trivial flavor flux,…
We obtain the elliptic curve and the Seiberg-Witten differential for an $N=2$ superconformal field theory which has an $E_8$ global symmetry at the strong coupling point $\tau=e^{\pi i/3}$. The differential has 120 poles corresponding to…
Six-dimensional superconformal field theories (SCFTs) give rise to four-dimensional (4d) ones when compactified on Riemann surfaces. In the $\mathcal{N}=(2,0)$ case, this yields the famous class S family. For $\mathcal{N}=(1,0)$ theories…
Supersymmetric theories with the same bosonic content but different fermions, aka \emph{twins}, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic $\mathcal{N}=3$ and…
Maximally $\mathcal{N}$ extended $2+1$ dimensional flat Supergravity theories exist for a class of super-Poincar\'{e} algebras for arbitrary $\mathcal{N}$. They have rich asymptotic structures and contain all interesting topological…
We show the existence of a global anomaly in the one-loop graphs of N=2 string theory, defined by sewing tree amplitudes, unless spacetime supersymmetry is imposed. The anomaly is responsible for the non-vanishing maximally helicity…
We classify the possible discrete (finite) symmetries of two--dimensional critical models described by unitary minimal conformally invariant theories. We find that all but six models have the group Z_2 as maximal symmetry. Among the six…
We describe conventional orientifold and orbifold quotients of string and M-theory in a unified approach based on exceptional field theory (ExFT). Using an extended spacetime, ExFT combines all the maximal ten and eleven dimensional…
Non-trivial extensions of the three dimensional Poincar\'e algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three dimensional generalizations of fractional supersymmetry of order…
There are two major ways of constructing 4d $\mathcal{N}=2$ superconformal field theories (SCFTs): the first one is putting a 6d $(2,0)$ theory on a punctured Riemann surface (class-S theory), and the second one is putting type IIB string…
6D spinors with $Spin(3,3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8(-24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations…
We uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field…
We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to…
In these lectures we discuss the supersymmetry algebra and its irreducible representations. We construct the theories of rigid supersymmetry and gave their superspace formulations. The perturbative quantum properties of the extended…
A new family of higher spin algebras that arises upon restricting matrix extensions of $\mathfrak{shs}[\lambda]$ is found. We identify coset CFTs realising these symmetry algebras, and thus propose new higher spin-CFT dual pairs. These…
For each $N$ an infinite number of Conformal Field Theories is presented that has the same fusion rules as SO(N) level 2. These new theories are obtained as extensions of the chiral algebra of $SO(NM^2)$ level 2, and correspond to new…
We provide a superselection theory of symmetry defects in 2+1D symmetry enriched topological (SET) order in the infinite volume setting. For a finite symmetry group $G$ with a unitary on-site action, our formalism produces a $G$-crossed…
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…
We prove that the family of non-linear $W$-algebras $SW(3/2,2)$ which are extensions of the $N=1$ superconformal algebra by a primary supercurrent of conformal weight $2$ can be realized as a quantum Hamiltonian reduction of the Lie…