Operator algebra

About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.

SCFT/VOA correspondence via Ω-deformation

Abstract: We investigate an alternative approach to the correspondence of four­ dimensional $$ \mathcal{N} $$ = 2 superconformal theories and two-dimensional vertex operator algebras, in the framework of the Ω-deformation of supersymmetric gauge theories. The two­dimensional Ω-deformation of the holomorphic-topological theory on the product four­ manifold is constructed at the level of supersymmetry variations and the action. The supersymmetric localization is performed to achieve a two-dimensional chiral CFT. The desired vertex operator algebra is recovered as the algebra of local operators of the resulting CFT. We also discuss the identification of the Schur index of the $$ \mathcal{N} $$ = 2 superconformal theory and the vacuum character of the vertex operator algebra at the level of their path integral representations, using our Ω-deformation point of view on the correspondence.

Noncommutative Field Theory from twisted Fock space

Abstract: We construct a quantum field theory in noncommutative space time by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative space time. The twisted Fock space and $S$-matrix consistent with this algebra have been constructed. The resultant $S$-matrix is consistent with that of Filk [Tomas Filk, Phys. Lett. B 376, 53 (1996).]. We find from this formulation that the spin-statistics relation is not violated in the canonical noncommutative field theories.

On Bell's inequalities and algebraic invariants

Abstract: Some algebraic invariants associated with Bell's inequalities are defined for inclusions of von Neumann algebras and studied within the context of general algebraic quantum theory. More special results are proven for quantum field theory which establish that these invariants take infinitely many values. Sharp short-distance bounds on the Bell correlations are also demonstrated in the context of relativistic quantum field theory.

Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, i

Abstract: We apply the general theory of tensor products of modules for a vertex operator algebra (developed by Lepowsky and the first author) and the general theory of intertwining operator algebras (developed by the first author) to the case of the N=1 superconformal minimal models and related models in superconformal field theory. We show that for the category of modules for a vertex operator algebra containing a subalgebra isomorphic to a tensor product of rational vertex operator superalgebras associated to the N =1 Neveu–Schwarz Lie superalgebra, the intertwining operators among the modules have the associativity property, the category has a natural structure of vertex tensor category, and a number of related results hold. We obtain, as a corollary and special case, a construction of a braided tensor category structure on the category of finite direct sums of minimal modules of central charge for the N = 1 Neveu–Schwarz Lie superalgebra for any fixed integers p, q larger than 1 such that p - q ∈ 2ℤ and (p - q)/2 and q relatively prime to each other.