Abstract
The main purpose of this paper is a mathematical construction of non-perturbative deformations of two-dimensional conformal field theories.We introduce the notion of a full vertex algebra which formulates a compact two-dimensional conformal field theory. Then, we construct a deformation family of full vertex algebras which serves as a current-current deformation of conformal field theory in physics. The parameter space of the deformations is expressed as a quotient of an orthogonal Grassmannian. This parameter space is a part of the CFT moduli space expected in physics. We demonstrate that nontrivial quotients of Grassmannians are obtained from holomorphic vertex operator algebras of central charge 24.
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