Liouville irregular states of half-integer ranks

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, Aeven) and (A1, Dodd) 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, D2n) to (A1, D2n−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.