The light asymptotic limit of conformal blocks in Toda field theory

TL;DR

This paper analyzes the light asymptotic limit of $A_{n-1}$ Toda conformal blocks using the AGT correspondence, revealing simplified Nekrasov partition functions and confirming results with conventional CFT methods.

Contribution

It introduces a method to compute Toda conformal blocks in the light limit via Nekrasov functions and verifies the results with traditional CFT calculations for $A_2$ case.

Findings

Nekrasov partition functions simplify to sums over restricted Young diagrams in the light limit.

Conformal blocks for $A_2$ Toda are computed with agreement between AGT and conventional methods.

The approach provides a new perspective on the structure of Toda conformal blocks in specific limits.

Abstract

We compute the light asymptotic limit of $A_{n-1}$ Toda conformal blocks by using the AGT correspondence. We show that for certain class of CFT blocks the corresponding Nekrasov partition functions in this limit are simplified drastically being represented as a sum of a restricted class of Young diagrams. In the particular case of $A_{2}$ Toda we also compute the corresponding conformal blocks using conventional CFT techniques finding a perfect agreement with the results obtained from the Nekrasov partition functions.