Room 326

On new exact conformal blocks and Nekrasov functions

Tanmoy Sengupta

IMSc

In 2016, an intriguing family of the one-point toric conformal
blocks AGT related to the N = 2∗ SU(2) Nekrasov functions was discovered by
M. Beccaria and G. Macorini. Members of the family are distinguished by
having only finite amount of poles as functions of the interme- diate
dimension/v.e.v. in gauge theory. Another remarkable property is that these
conformal blocks/Nekrasov functions can be found in closed form to all
orders in the coupling expansion. Same year, Nikita Nemkov showed that we
can use Zamolodchikov’s recurrence equation to systematically account for
these exceptional conformal blocks. We can show that the family is
infinite-dimensional and describe the corresponding parameter set. We can
further apply the developed technique to demonstrate that the four-point
spheric conformal blocks feature analogous exact expressions. We will also
discuss the modular transformations of the finite-pole blocks.

References: arXiv IDs -- 1606.05324, 1606.00179.