相关论文: Some cohomology operators in 2-D field theory
We consider correlation functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We describe a generalisation of genus one Zhu recursion where we express an arbitrary genus two $n$--point…
We advance a correspondence between the topological defect operators in Liouville and Toda conformal field theories - which we construct - and loop operators and domain wall operators in four dimensional N=2 supersymmetric gauge theories on…
We study Lie conformal algebroids (LCAd) and their representations using the language of lambda-brackets and Lie conformal algebras. We describe several general constructions, such as the LCAd of conformal derivations CDer(A) of a…
In this manuscript, we will study both $\tilde{o}$-convergence in (partially) ordered vector spaces and a kind of convergence in a vector space $V$. A vector space $V$ is called semi-order vector space (in short semi-order space), if there…
We prove that all nice holomorphic vertex operator superalgebras (VOSAs) with central charge at most 24 and with non-trivial odd part are unitary, apart from the hypothetical ones arising as fake copies of the shorter moonshine VOSA or of…
A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…
Dirac cohomology is a new tool to study unitary and admissible representations of semisimple Lie groups. It was introduced by Vogan and further studied by Kostant and ourselves \cite{V2}, \cite{HP1}, \cite{Kdircoh}. The aim of this paper is…
The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…
Invited talk at the International Symposium on Generalized Symmetries in Physics at the Arnold-Sommerfeld-Institute, Clausthal, Germany, July 26 -- July 29, 1993. This talk reviews results on the structure of algebras consisting of…
We introduce a symmetric operad whose algebras are the Operator Product Expansion (OPE) Algebras of quantum fields. There is a natural classical limit for the algebras over this operad and they are commutative associative algebras with…
It is known from Zhu's results that under modular transformations, correlators of rational $C_2$-cofinite vertex operator algebras transform like Jacobi forms. We investigate the modular transformation properties of VOA correlators that…
We introduce two $K$-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these…
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…
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…
We study properties of a C_2-cofinite vertex operator algebra of CFT type. If it is also rational and V'\cong V, then the rigidity of the tensor category of modules has been proved by Huang. When we treat an irrational C_2-cofinite VOA, the…
We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…
The main topic of this paper is two folds. First, we compute the first relative cohomology group of the Lie algebra of smooth vector fields on the projective line, Vect(RP^1), with coefficients in the space of bilinear differential…
We present the results of computation of cohomology for some Lie (super)algebras of Hamiltonian vector fields and related algebras. At present, the full cohomology rings for these algebras are not known even for the low dimensional vector…
A Beilinson completion algebra (BCA) A is a complete semilocal algebra over a perfect field k, whose residue fields are high dimensional local fields. In addition A is a semi-topological algebra. The completion of the structure sheaf of an…
The correlators of free four dimensional conformal field theories (CFT4) have been shown to be given by amplitudes in two-dimensional $so(4,2)$ equivariant topological field theories (TFT2), by using a vertex operator formalism for the…