Revisiting the Computation of Cohomology Classes of the Witt Algebra Using Conformal Field Theory and Aspects of Conformal Algebra
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In this article, the author revisited some aspects of the computations of the cohomology class of H2 (Witt, C) using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional central extension of the Witt algebra to the Virasoro algebra.Abstract:
In this article, we revisit some aspects of the
computation of the cohomology class of H2 (Witt, C) using some methods in
two-dimensional conformal field theory and conformal algebra to obtain the
one-dimensional central extension of the Witt algebra to the Virasoro algebra.
Even though this is well-known in the
context of standard mathematical physics literature, the operator product
expansion of the energy-momentum tensor in two-dimensional conformal
field theory is presented almost axiomatically. In this paper, we attempt to
reformulate it with the help of a suitable modification of conformal algebra (as
developed by V. Kac), and apply it to
compute the representative element of the cohomology class which gives the
desired central extension. This paper was written in the scope of an
undergraduate’s exploration of conformal field theory and to gain insight on
the subject from a mathematical perspective.read more
References
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Book
Introduction to Lie Algebras and Representation Theory
TL;DR: In this paper, Semisimple Lie Algebras and root systems are used for representation theory, isomorphism and conjugacy theorem, and existence theorem for representation.
Book
Vertex algebras for beginners
TL;DR: In this paper, a formal distribution a(z,w) = 2 QFT and chiral algebras is defined and the Virasoro algebra is defined, which is a generalization of the Wightman axioms.
Journal ArticleDOI
Cohomology Theory of Lie Groups and Lie Algebras
TL;DR: In this paper, the authors give a systematic treatment of the methods by which topological questions concerning compact Lie groups may be reduced to algebraic questions concerning Lie algebras.
BookDOI
The geometry of infinite-dimensional groups
Boris Khesin,Robert Wendt +1 more
TL;DR: In this article, infinite-dimensional Lie groups are used for topological and Holomorphic Gauge Theories, and applications of groups are discussed. But they do not cover the application of Lie groups in topological topology.