Liouville Irregular States of Half-Integer Ranks

2024/01/26 by Hamachika, Ryo, Nakanishi, Tomoki, Nishinaka, Takahiro +1 · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2401.14662

Abstract

We conjecture a set of differential equations that characterizes the Liouville irregular states of half-integer ranks, which extends the generalized AGT correspondence to all the (A₁,A_even) and (A₁,D_odd) types Argyres-Douglas theories. For lower half-integer ranks, our conjecture is verified by deriving it as a suitable limit of a similar set of differential equations for integer ranks. This limit is interpreted as the 2D counterpart of a 4D RG-flow from (A₁,D_2n) to (A₁,D_2n-1). For rank 3/2, we solve the conjectured differential equations and find a power series expression for the irregular state |I^(3/2)⟩. For rank 5/2, our conjecture is consistent with the differential equations recently discovered by H. Poghosyan and R. Poghossian.

Cited by

• A note on half-integer irregular representations of Virasoro algebra

Related

• A note on rank 5/2 Liouville irregular block, Painlevé 1 and the \cal H₀ Argyres-Douglas theory
• A note on rank (3)/(2) Liouville irregular block
• On irregular states and Argyres-Douglas theories
• A note on half-integer irregular representations of Virasoro algebra
• Approaching Argyres-Douglas theories