Liouville irregular states of half-integer ranks

Abstract

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 (A 1 , A even) and (A 1 , 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 (A 1 , D 2n ) to (A 1 , 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.

Keywords

• Supersymmetry and Duality
• Conformal Field Models in String Theory
• Extended Supersymmetry