Related papers: Conformal nets from minimal W-algebras
We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…
We prove the first nontrivial reconstruction theorem for modular tensor categories: the category associated to any twisted Drinfeld double of any finite group, can be realised as the representation category of a completely rational…
We give an exposition on the current status of classification of operator algebraic conformal field theories. We explain roles of complete rationality and alpha-induction for nets of subfactors in such a classification and present the…
This paper is part of an effort to gain further understanding of 2D Logarithmic Conformal Field Theories (LCFTs) by exploring their lattice regularizations. While all work so far has dealt with the Virasoro algebra (or the product of left…
In this paper, extensions of nonunitary rational Virasoro vertex operator algebras corresponding to some exceptional modular invariants are constructed. The uniqueness of these extensions is also established.
We discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro nets). In particular we classify the local…
We present subsingular vectors of the N=2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the…
All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use subfactor theory and…
We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex…
In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten theory with many new recent developments in the sheaf theoretic context. In this paper, we rephrase the sheaf-theoretic Virasoro constraints in terms of…
We build unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using induced representations as a guide. Our prescription naturally emerges from an ultrarelativistic limit of highest-weight…
We consider conformal nets on $S^1$ of von Neumann algebras, acting on the full Fock space, arising in free probability. These models are twisted local, but non-local. We extend to the non-local case the general analysis of the modular…
In this paper, we give a unified construction of vertex algebras arising from infinite-dimensional Lie algebras, including the affine Kac-Moody algebras, Virasoro algebras, Heisenberg algebras and their higher rank analogs, orbifolds and…
In this paper, we first give the definiton of a vertex superalgebroid. Then we construct a family of vertex superalgebras associated to vertex superalgebroids. As a main result, we find a sufficient and necessary condition that this vertex…
In this paper, we study the $U(1)^2$ Kac--Moody algebra and generalize the standard Sugawara construction of the Virasoro algebra to an infinite family of new realizations. In this case, in addition to the standard invariant tensor…
We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between…
We develop a calculus of variations for functionals on certain spaces of conformal maps. Such a space \Omega\ is composed of all maps that are conformal on domains containing a fix compact annular set of the Riemann sphere, and that are…
In this paper, we introduce a new family of functors from the category of modules for the Weyl algebra to the category of modules for the super-Virasoro algebras. The properties of these functors are investigated, with an emphasis on…
In this paper, we prove classical affine W-algebras associated to Lie superalgebras (W-superalgebras) can be constructed in two different ways: via affine classical Hamiltonian reductions and via taking quasi-classical limits of quantum…
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…