Abstract
We study certain exactly marginal gaugings involving arbitrary numbers of Argyres-Douglas (AD) theories and show that the resulting Schur indices are related to those of certain Lagrangian theories of class mathcal{S} via simple transformations. By writing these quantities in the language of 2D topological quantum field theory (TQFT), we easily read off the S-duality action on the flavor symmetries of the AD quivers and also find expressions for the Schur indices of various classes of exotic AD theories appearing in different decoupling limits. The TQFT expressions for these latter theories are related by simple transformations to the corresponding quantities for certain well-known isolated theories with regular punctures (e.g., the Minahan-Nemeschansky E6 theory and various generalizations). We then reinterpret the TQFT expressions for the indices of our AD theories in terms of the topology of the corresponding 3D mirror quivers, and we show that our isolated AD theories generically admit renormalization group (RG) flows to interacting superconformal field theories (SCFTs) with thirty-two (Poincaré plus special) supercharges. Motivated by these examples, we argue that, in a sense we make precise, the existence of RG flows to interacting SCFTs with thirty-two supercharges is generic in a far larger class of 4D mathcal{N} = 2 SCFTs arising from compactifications of the 6D (2, 0) theory on surfaces with irregular singularities.
Highlights
Theories, where G is the ADE flavor symmetry of the superconformal field theories (SCFTs)
By writing these quantities in the language of 2D topological quantum field theory (TQFT), we read off the S-duality action on the flavor symmetries of the AD quivers and find expressions for the Schur indices of various classes of exotic AD theories appearing in different decoupling limits
We reinterpret the TQFT expressions for the indices of our AD theories in terms of the topology of the corresponding 3D mirror quivers, and we show that our isolated AD theories generically admit renormalization group (RG) flows to interacting superconformal field theories (SCFTs) with thirty-two (Poincare plus special) supercharges
Summary
Consider AD2n+ and AD2n+3 for a positive integer n and an odd positive integer (so that 2n + and 2n + 3 are odd) These theories have SU(2n + ) and SU(2n + 3 ) flavor symmetries respectively. The resulting theory is an N = 2 SCFT described by the quiver diagram in figure 1 and has U(n) × U(n + 2 ) flavor symmetry. Given this flavor symmetry, we can further gauge an SU(n + 2 ) ⊂ U(n + 2 ) subgroup. ≥ 1 fundamental hypermultiplets (recall that ∈ Zodd) This theory has U(n1) × U(n2) × U( ) × U(1) 2n−n1−n2 −2 flavor symmetry. Where the middle n in the subscript stands for the largest rank of the simple components of the gauge group
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