Exact expressions for the 5-Point Liouville conformal block with a level-two degenerate field insertion

by Hasmik Poghosyan (Yerevan Physics Institute)

Monday 6 Oct 2025, 14:00 → 15:00 Europe/Rome

Aula Grassano

In this talk I will  investigate  the  5-point Liouville conformal block with a level 2 degenerate field insertion. The main tool is the BPZ differential equation, which, upon placing three of the insertions at the standard positions ∞, 1, and 0, reduces to a linear differential equation which is of order two in the degenerate insertion point z, and order one in the remaining point x. We will see that the solution can be expressed in terms of a single hypergeometric function and its derivative, with coefficients computable (up to the desired order x^k) via a recursion relation.
This new representation makes it straightforward to relate different asymptotic regions. As a by-product, this provides us a simple derivation of fusion and braiding coefficients. I will also describe the subtle procedure of merging the degenerate field with the outgoing state, thereby obtaining a generic 4-point block.