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It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we introduce a notion of a framed algebra, which is a finite-dimensional non-associative algebra, and showed that the category of framed algebras and the category of code conformal field theories are equivalent. We have also constructed a new family of integrable conformal field theories using this equivalence. These conformal field theories are expected to be useful for the study of moduli spaces of conformal field theories.
The role of automorphisms of infinite-dimensional Lie algebras in conformal field theory is examined. Two main types of applications are discussed; they are related to the enhancement and reduction of symmetry, respectively. The structures one encoun
The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of any rational
The idea of summing over all intermediate states that is central for implementing locality in quantum systems can be realized by coend constructions. In the concrete case of systems of conformal blocks for a certain class of conformal vertex algebras
Given formal differential operators $F_i$ on polynomial algebra in several variables $x_1,...,x_n$, we discuss finding expressions $K_l$ determined by the equation $exp(sum_i x_i F_i)(exp(sum_j q_j x_j)) = exp(sum_l K_l x_l)$ and their applications.
Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken as a reduced quantum plane, we build a differential calculus Omega(S) on the quantum space S defined by the algebra C^infty(M) otimes M(3,C), where M is a space-time manifo