Speaker
Description
The Virasoro algebra has long played a central role in string theory and two-dimensional conformal field theory. It is therefore somewhat surprising that explicit expressions for several foundational objects have remained unknown for so long. In this talk, we present recent progress in this direction. By studying the inverse Shapovalov form (also known as the inverse Gram matrix), we derive explicit expressions for four key structures associated with the Virasoro algebra: the resolution of the identity, the operator product expansion, the Casimir operator, and the conformal blocks. The first three are expressed in terms of the algebra’s null vectors, while the conformal blocks are obtained as a new series expansion with fully explicit coefficients.