Related papers: Vertex Algebra constructions for (analytic) Geomet…
We give a functorial construction of the genus zero chiral algebras of class $\mathcal{S}$, that is, the vertex algebras corresponding to the theory of class $\mathcal{S}$ associated with genus zero pointed Riemann surfaces via the 4d/2d…
Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE,…
Vertex algebras and factorization algebras are two approaches to chiral conformal field theory. Costello and Gwilliam describe how every holomorphic factorization algebra on the plane of complex numbers satisfying certain assumptions gives…
Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the…
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers.
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
In the framework of bidifferential graded algebras, we present universal solution generating techniques for a wide class of integrable systems.
We describe explicitly the vertex algebra of (twisted) chiral differential operators on certain nilmanifolds and construct their logarithmic modules. This is achieved by generalizing the construction of vertex operators in terms of…
We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the…
We give a short introduction to generalized vertex algebras, using the notion of polylocal fields. We construct a generalized vertex algebra associated to a vector space h with a symmetric bilinear form. It contains as subalgebras all…
Vertex algebras are equivalent to translation-equivariant chiral algebras on $\mathbb{A}^1$, in the sense of Beilinson and Drinfeld. In this paper we give an algebraic construction of a chiral algebra on $\mathbb{A}^n$; this can be seen as…
For an infinite chain bicomplex we show that the orthogonality and grading conditions provide it with the structure of a bigraded differential algebra with respect to a natural multiplication of several elements bicomplex spaces.…
We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the following conditions: (i) the weight of any nonzero…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
We present explicit global constructions - avoiding power series - of certain chiral CFTs, including current algebras on the projective line. We outline an approach to vertex algebras, inspired by this construction. We construct natural…
We study gravitational algebras on spacetimes with two extremal surfaces. In the example of a long wormhole with two asymptotic AdS boundaries and two compact extremal surfaces, we discuss the assignment of gravitational algebras to various…
We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are associated to junctions of two boundary conditions in a 4d…
We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.
This note serves two purposes: 1) define actions by differential graded Lie algebras, and 2) apply such differential graded Lie symmetry in general relativity (GR) to constrain the spacetime geometry on a neighborhood of infinity.
Geometric vertex algebras are a simplified version of Huang's geometric vertex operator algebras. We give a self-contained account of the equivalence of geometric vertex algebras with Z-graded vertex algebras.