Chennai Mathematical Institute


Date and time: Friday, April 2, 3 pm
Virasoro Blocks and Modular Structures

Madhusudhan Raman


This is the last of three lectures that will discuss aspects of two-dimensional conformal field theories. We analyze Virasoro conformal blocks in the regime of heavy exchange dimension, i.e. we solve the Zamolodchikov h-recursion order-by-order. For the 1-point block on the torus and the 4-point block on the sphere, we show that each order in the large-h expansion can be written in closed form as polynomials in the Eisenstein series. The appearance of this structure is explained using the fusion kernel and, more markedly, by invoking the modular anomaly equations via the 2d/4d correspondence. We observe that the existence of these constraints allows us to develop a faster algorithm to recursively construct the blocks in this regime.