32 research outputs found
Noncommutative Root Space Witt, Ricci Flow, and Poisson Bracket Continual Lie Algebras
We introduce new examples of mappings defining noncommutative root space
generalizations for the Witt, Ricci flow, and Poisson bracket continual Lie
algebras
Sewn sphere cohomologies for vertex algebras
summary:We define sewn elliptic cohomologies for vertex algebras by sewing procedure for coboundary operators
Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
We define the partition and -point correlation functions for a vertex
operator superalgebra on a genus two Riemann surface formed by sewing two tori
together. For the free fermion vertex operator superalgebra we obtain a closed
formula for the genus two continuous orbifold partition function in terms of an
infinite dimensional determinant with entries arising from torus Szeg\"o
kernels. We prove that the partition function is holomorphic in the sewing
parameters on a given suitable domain and describe its modular properties.
Using the bosonized formalism, a new genus two Jacobi product identity is
described for the Riemann theta series. We compute and discuss the modular
properties of the generating function for all -point functions in terms of a
genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one
point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun.
Math. Phy
Torus n-Point Functions for -graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds
We consider genus one n-point functions for a vertex operator superalgebra
with a real grading. We compute all n-point functions for rank one and rank two
fermion vertex operator superalgebras. In the rank two fermion case, we obtain
all orbifold n-point functions for a twisted module associated with a
continuous automorphism generated by a Heisenberg bosonic state. The modular
properties of these orbifold n-point functions are given and we describe a
generalization of Fay's trisecant identity for elliptic functions.Comment: 50 page
Twisted Frobenius Identities from Vertex Operator Superalgebras
In consideration of the continuous orbifold partition function and a generating function for all n-point correlation functions for the rank two free fermion vertex operator superalgebra on the self-sewing torus, we introduce the twisted version of Frobenius identity
Ward identities from recursion formulas for correlation functions in conformal field theory
summary:A conformal block formulation for the Zhu recursion procedure in conformal field theory which allows to find -point functions in terms of the lower correlations functions is introduced. Then the Zhu reduction operators acting on a tensor product of VOA modules are defined. By means of these operators we show that the Zhu reduction procedure generates explicit forms of Ward identities for conformal blocks of vertex operator algebras. Explicit examples of Ward identities for the Heisenberg and free fermionic vertex operator algebras are supplied
Sine-Gordon model in the homogeneous higher grading
A construction of equations and solutions for the sine-Gordon model in the homogeneous grading as an example of higher grading a ne Toda models are considered