Reimundo Heluani
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View article: Chiral homology of the projective line and extensions of vertex algebra modules
Chiral homology of the projective line and extensions of vertex algebra modules Open
The purpose of this note is to establish an isomorphism from the vector space of extensions between two modules over a vertex algebra, to an appropriate first chiral homology of one dimensional projective space with coefficients in the cor…
View article: Conformal operads and the basic vertex algebra cohomology complex
Conformal operads and the basic vertex algebra cohomology complex Open
We develop the notion of a (pro-) conformal pseudo operad and apply it to the construction of the basic cohomology complex of a vertex algebra. The paper heavily uses the ideas and constructions of the work of Tamarkin [Tam02]
View article: A Hodge filtration on chiral homology and Poisson homology of associated schemes
A Hodge filtration on chiral homology and Poisson homology of associated schemes Open
We introduce filtrations in chiral homology complexes of smooth elliptic curves, exploiting the mixed Hodge structure on cohomology groups of configuration spaces. We use these to relate the chiral homology of a smooth elliptic curve with …
View article: The Singular Support of the Ising Model
The Singular Support of the Ising Model Open
We prove a new quasiparticle sum expression for the character of the Ising model vertex algebra, related to the Jackson–Slater $q$-series identity of Rogers–Ramanujan type and to Nahm sums for the matrix $\left (\begin {smallmatrix}8&3\\3&…
View article: Noncommutative Poisson vertex algebras and Courant-Dorfman algebras
Noncommutative Poisson vertex algebras and Courant-Dorfman algebras Open
We introduce the notion of double Courant-Dorfman algebra and prove that it satisfies the so-called Kontsevich-Rosenberg principle, that is, a double Courant-Dorfman algebra induces Roytenberg's Courant-Dorfman algebras on the affine schem…
View article: The First Chiral Homology Group
The First Chiral Homology Group Open
We study the first chiral homology group of elliptic curves with coefficients in vacuum insertions of a conformal vertex algebra V. We find finiteness conditions on V guaranteeing that these homologies are finite dimensional, generalizing …
View article: Classical and variational Poisson cohomology
Classical and variational Poisson cohomology Open
We prove that, for a Poisson vertex algebra V, the canonical injective homomorphism of the variational cohomology of V to its classical cohomology is an isomorphism, provided that V, viewed as a differential algebra, is an algebra of diffe…
View article: On a Complex-Symplectic Mirror Pair
On a Complex-Symplectic Mirror Pair Open
We study the canonical Poisson structure on the loop space of the super-double-twisted-torus and its quantization. As a consequence we obtain a rigorous construction of mirror symmetry as an intertwiner of the N=2 super-conformal structure…