Argyres-Douglas theories and Liouville irregular states

Abstract

We study irregular states of rank-two and three in Liouville theory, based on an ansatz proposed by D. Gaiotto and J. Teschner. Using these irregular states, we evaluate asymptotic expansions of irregular conformal blocks corresponding to the partition functions of (A 1 , A 3 ) and (A 1 , D 4 ) Argyres-Douglas theories for general Ω-background parameters. In the limit of vanishing Liouville charge, our result reproduces strong coupling expansions of the partition functions recently obtained via the Painlevé/gauge correspondence. This suggests that the irregular conformal block for one irregular singularity of rank 3 on sphere is also related to Painlevé II. We also find that our partition functions are invariant under the action of the Weyl group of flavor symmetries once four and two-dimensional parameters are correctly identified. We finally propose a generalization of this parameter identification to general irregular states of integer rank.

Defect a-theorem and a-maximization

“…To prove the formulas (4.37) for codimension-two defects in general (2, 0) SCFTs requires a derivation of the corresponding defect 't Hooft anomalies, by extending the work of [113] to cases with an M-theory orientifold (for g = D n ), and by studying inflow in IIB string theory with ADE singularities [116]. Before ending this section, we note that beyond the family of the D ϕ [g] defects which define regular (tame) punctures in the class S setup, the 6d (2, 0) SCFTs admit a much larger zoo of superconformal codimension-two defects that give rise to irregular (wild) punctures where the superconformal symmetry is emergent in the IR [37,[117][118][119][120][121][122], as well as the twisted defects (punctures) which are attached to codimension-one topological defects generating the outer-automorphism symmetry of certain (2, 0) theories [109,[123][124][125][126][127][128][129]. More recently, codimension-two defects in 6d N = (1, 0) SCFTs including the Estring theory have also been analyzed [130][131][132][133][134][135].…”

Argyres-Douglas theories, S-duality and AGT correspondence

“…While the partition functions of conformally gauged AD theories have not been evaluated, there exists a series of non-conformally gauged AD theories whose partition functions were evaluated via a generalization [17,18] of the AGT correspondence [19,20] (See [21][22][23][24][25][26][27][28][29][30] for recent developments on this generalization). In particular, for the theory described by the quiver in figure 2, the partition function was evaluated as the inner product of so-called "irregular states" of Virasoro algebra.…”

“…Note that the perturbative part contains the prepotential of the (A1, D4) theories (with their flavor symmetries ungauged) 18. The 1/c1-expansion of a|I(2) was carefully studied in[30].…”

Argyres-Douglas Theories, S-duality and AGT Correspondence

“…inst (q 2 , a) , (5.19) at least up to O(q 8 ). 18 The 1/c 1 -expansion of a|I (2) was carefully studied in [27].…”

“…While the partition functions of conformally gauged AD theories have not been evaluated, there exists a series of non-conformally gauged AD theories whose partition functions were evaluated via a generalization [14,15] of the AGT correspondence [16,17] (See [18][19][20][21][22][23][24][25][26][27] (A 1 , D 2n )…”