Related papers: Exceptional Algebra and Sporadic Groups at c=12
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
In this note we study four dimensional theories with N=3 superconformal symmetry, that do not also have N=4 supersymmetry. No examples of such theories are known, but their existence is also not ruled out. We analyze several properties that…
We find all exceptional spin groups attached to the vertices of any exceptional spin graph on any hyperbolic Riemann surface S of genus g>1. In particular, we show that when the order r of a graph is r>2 (i.e.the genus of S must be g>3)…
We construct 7-dimensional quantum field theories encoding the anomalies of conformal field theories with (2,0) supersymmetry in six dimensions. We explain how the conformal blocks of the (2,0) theories arise in this context. A result of…
It is expected on general grounds that the moduli space of 4d $\mathcal{N}=3$ theories is of the form $\mathbb{C}^{3r}/\Gamma$, with $r$ the rank and $\Gamma$ a crystallographic complex reflection group (CCRG). As in the case of Lie…
We explore the constraints on the spectrum of primary fields implied by modularity of the elliptic genus of N=(2,2) 2D CFT's. We show that such constraints have nontrivial implications for the existence of "extremal" N=(2,2) conformal field…
Within the framework of four dimensional conformal supergravity we consider $\mathcal{N}=1,2,3,4$ supersymmetric theories generally twisted along the abelian subgroups of the R-symmetry and possibly other global symmetry groups. Upon…
A new matrix model is described, based on the exceptional Jordan algebra. The action is cubic, as in matrix Chern-Simons theory. We describe a compactification that, we argue, reproduces, at the one loop level, an octonionic…
Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. The 12-dimensional EFT associated to the group $SL(2)\times\mathbb{R}^+$ together with its action is…
These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…
We study two-dimensional celestial conformal field theory describing four-dimensional ${\cal N}=1$ supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct…
By generalizing a fermionic construction, a natural relation is found between SL(2) degenerate conformal field theories and some N=2 discrete superconformal series. These non-unitary models contain, as a subclass, N=2 minimal models. The…
We elucidate the correspondence between a particular class of superconformal field theories in six dimensions and homomorphisms from discrete subgroups of $SU(2)$ into $E_8$, as predicted from string dualities. We show how this match works…
The generalized symmetric space sine-Gordon theories are a series of 1+1-integrable field theories that are classically equivalent to superstrings on symmetric space spacetimes F/G. They are formulated in terms of a semi-symmetric space as…
We present evidence for a new class of strongly coupled N = 1 superconformal field theories (SCFTs) motivated by F-theory GUT constructions. These SCFTs arise from D3-brane probes of tilted seven-branes which undergo monodromy. In the probe…
Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…
An algebraic description of basic discrete symmetries (space inversion P, time reversal T, charge conjugation C and their combinations PT, CP, CT, CPT) is studied. Discrete subgroups {1,P,T,PT} of orthogonal groups of multidimensional…
This is the second part of the work where quasi-modular forms emerge from small exotic smooth $\mathbb{R}^4$'s grouped in a fixed radial family. SU(2) Seiberg-Witten theory when formulated on exotic $\mathbb{R}^4$ from the radial family, in…
We study the problem of finding exactly marginal deformations of N=1 superconformal field theories in four dimensions. We find that the only way a marginal chiral operator can become not exactly marginal is for it to combine with a…
The use of the AdS/CFT correspondence to arrive at quiver gauge field theories is dicussed, focusing on the orbifolded case without supersymmetry. An abelian orbifold with the finite group $Z_{p}$ can give rise to a $G = SU(N)^p$ gauge…