Peculiar index relations, 2D TQFT, and universality of SUSY enhancement

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 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 E 6 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 N = 2 SCFTs arising from compactifications of the 6D (2, 0) theory on surfaces with irregular singularities.1 Although note that the simplest example, D 2 (SU (3)), was originally constructed in [2].at local Calabi-Yau singularities and are part of a larger class of theories called the D p (G) theories, where G is the ADE flavor symmetry of the SCFT. However, using the methods of [3], we will primarily think of these theories as coming from twisted compactifications of the 6D (2, 0) theory on Riemann surfaces with an irregular puncture. 2 While the strongly coupled D 2 (SU (2n + 1)) SCFTs are of Argyres-Douglas (AD) type 3 and therefore lack N = 2 Lagrangians, they behave in various surprising ways like collections of free hypermultiplets:• The role of the D 2 (SU (3)) theory in the S-duality studied in [4-6] is reminiscent of the role played by some of the hypermultiplets in the S-duality of N = 2 SU (3) Supersymmetric Quantum Chromodynamics (SQCD) with N f = 6 flavors [7].• The so-called "Schur" limits of the 4D N = 2 superconformal indices of the D 2 (SU (2n+ 1)) theories are related to the Schur indices of free hypermultiplets by a simple rescaling of the superconformal fugacity and a specialization of the flavor fugacities [8,9].• The (partially refined) Schur indices of the D 2 (SU (2n + 1)) theories can be computed via theories of free non-unitary hypermultiplets with wrong statistics in 4D [10].Given these parallels, it is interesting to ask if at least some of these close relations with Lagrangian theories persist upon conformally gauging subgroups of the flavor symmetry of the D 2 (SU (2n + 1)) theories. As we will see below, the answer to this question is a resounding, "yes." In particular, we will show ...

Argyres-Douglas theories, S-duality and AGT correspondence

“…We use (1.3) and (1.4) to show in particular that the S-duality of the (A 3 , A 3 ) theory is in a peculiar relation to that of SU(2) gauge theory with 4 fundamental flavors. It is an interesting open problem to see how this peculiar relation is connected to a similar relation between the Schur index of the same pair of theories discussed in [35].…”

“…• It was shown in [35] that the Schur indices of the (A 3 , A 3 ) theory and SU(2) gauge theory with four flavors are related by a change of variables involving q → q 2 , (6.3)…”

3d mirrors of the circle reduction of twisted A2N theories of class S

“…First of all, a similar technique was used by the authors of [68,69] to study various supersymmetry enhancement RG flows from theories with 16 supercharges to those with 32 supercharges. It was shown in [69] that this type of RG flows is generic in a certain class (known as type III in the nomenclature of [4]) of the 4d N = 2 theories. Secondly, as pointed out in [68], one could be more cautious about the above conclusion whether the 4d theory in question needs to be N = 4 SYM.…”

1-form symmetry, isolated $$ \mathcal{N} $$ = 2 SCFTs, and Calabi-Yau threefolds

“…Regarding the second point in the previous paragraph, we are not aware of gauge coupling interpretations for most of the conformal manifolds we will come across, but we are also not aware of arguments forbidding such interpretations (similar comments apply to the vast majority of the theories discussed in[17,18]). Indeed, there are conjectures that an N = 2-preserving exactly marginal deformation always corresponds to a gauge coupling[19,20] 4.…”