TITLE:
Revisiting the Computation of Cohomology Classes of the Witt Algebra Using Conformal Field Theory and Aspects of Conformal Algebra
AUTHORS:
Jacksyn Bakeberg, Parthasarathi Nag
KEYWORDS:
Conformal Field Theory, Conformal Algebra, Witt Algebra, Central Extension, Virasoro Algebra
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.3,
March
25,
2019
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.