A note on rank 3/2 Liouville irregular block

A bstract This paper focuses on a conformal block with rank 3/2 3 2 irregular singularity which corresponds to the prepotential of the H₁ H 1 Argyres-Douglas theory in Ω background. We derive this irregular conformal block using the generalized holomorphic anomaly recursion relation. This results in an expression which is a power series in Ω-background parameters ϵ 1 , 2 and exact in coupling. We have verified that in the small coupling regime our result is consistent with previously known expressions. Furthermore we derive the Deformed Seiberg-Witten curve which provides an alternative tool to explore the above mentioned theory in Nekrasov-Shatashvili limit of Ω-background. We checked that the results are in complete agreement with the holomorphic anomaly approach.