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

We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the…

In this note we determine the graviton-graviton OPE and the null states in any $w_{1+\infty}$ symmetric theory on the celestial sphere. Our analysis shows that there exists a discrete \textit{infinite} family of such theories. The…

Classically important examples of Lie superalgebras have been constructed starting from the Witt and Virasoro algebra. In this article we consider Lie superalgebras of Krichever-Novikov type. These algebras are multi-point and higher genus…

This survey reports on current progress of programs to classify graph C*-algebras and Leavitt path algebras up to Morita equivalence using K-theory. Beginning with an overview and some history, we trace the development of the classification…

In this review we discuss currents in celestial CFT and the consistency of their naive symmetry algebras. In particular we study in detail the Jacobi identity and the double residue condition for soft insertions, hard momentum space…

Every 4d $\mathcal{N} = 2$ SCFT $\mathcal{T}$ corresponds to an associated VOA $\mathbb{V}(\mathcal{T})$, which is in general non-rational with a more involved representation theory. Null states in $\mathbb{V}(\mathcal{T})$ can give rise to…

All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete…

Motivated by applications of twisted current algebras in description of the entropy of $Ads_3$ black hole, we investigate the simplest twisted current algebra $sl(3,{\bf C})^{(2)}_k$. Free field representation of the twisted algebra and the…

We consider the most general SU(3) singlet space of gauged N=8 supergravity in four-dimensions. The SU(3)-invariant six scalar fields in the theory can be viewed in terms of six real four-forms. By exponentiating these four-forms, we…

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra…

Let g denote a Lie algebra over a field of characteristic zero, and let T(g) denote the tensor product of g with a ring of truncated polynomials. The Lie algebra T(g) is called a truncated current Lie algebra, or in the special case when g…

The effective field theory likelihood for the density field of biased tracers allows for cosmology inference from the clustering of galaxies that consistently uses all available information at a given order in perturbation theory. This…

In radial quantization, the ground states of a gauge theory on ADE singularities $\mathbb{R}^4/\Gamma$ are characterized by flat connections that are maps from $\Gamma$ to the gauge group. We study Class $\mathcal{S}$ theory of type…

We present new $AdS_5$ solutions in 11d supergravity and identify them as the gravity duals of a class of 4d $\mathcal N = 2$ SCFTs of Argyres-Douglas type, engineered by a stack of M5-branes wrapped on a sphere with one irregular puncture…

We give a minimal system of 476 generators (resp. 510 generators) for the algebra of SL(2,C)-covariant polynomials on binary forms of degree 9 (resp. degree 10). These results were only known as conjectures so far. The computations rely on…

Using Furuta's idea of finite dimensional approximation in Seiberg-Witten theory, we refine Seiberg-Witten Floer homology to obtain an invariant of homology 3-spheres which lives in the S^1-equivariant graded suspension category. In…

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra…

These lecture notes cover the Standard Model (SM) course for Part III of the Cambridge Mathematical Tripos, taught during the years 2020-2023. The course comprised 25 lectures and 4 example classes. Following a brief historical…

We demonstrate that flavour-changing neutral currents in the top sector, mediated by leptophilic scalars at the electroweak scale, can easily arise in scenarios of new physics, and in particular in composite Higgs models. We moreover show…

Self-consistent (non-)abelian statistics in 2+1D are classified by modular tensor categories (MTC). In recent works, a simplified axiomatic approach to MTCs, based on fusion coefficients $N^{ij}_k$ and spins $s_i$, was proposed. A numerical…