Revisiting the computation of cohomology classes of the Witt algebra using conformal field theory and aspects of conformal algebra

Jacksyn Bakeberg, Parthasarathi Nag

Published 2018-08-09Version 1

In this article, we revisit some aspects of the computation of the cohomology class of $H^2 ( \text{Witt}, \mathbb{C})$ 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.