$$ \mathcal{N} $$ = 1 conformal dualities

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139

We consider compactifications of 6d minimal (D N +3 , D N +3 ) type conformal matter SCFTs on a generic Riemann surface. We derive the theories corresponding to three punctured spheres (trinions) with three maximal punctures, from which one can construct models corresponding to generic surfaces. The trinion models are simple quiver theories with N = 1 SU (2) gauge nodes. One of the three puncture non abelian symmetries is emergent in the IR. The derivation of the trinions proceeds by analyzing RG flows between conformal matter SCFTs with different values of N and relations between their subsequent reductions to 4d. In particular, using the flows we first derive trinions with two maximal and one minimal punctures, and then we argue that collections of N minimal punctures can be interpreted as a maximal one. This suggestion is checked by matching the properties of the 4d models such as 't Hooft anomalies, symmetries, and the structure of the conformal manifold to the expectations from 6d. We then use the understanding that collections of minimal punctures might be equivalent to maximal ones to construct trinions with three maximal punctures, and then 4d theories corresponding to arbitrary surfaces, for 6d models described by two M 5 branes probing a Z k singularity. This entails the introduction of a novel type of maximal puncture. Again, the suggestion is checked by matching anomalies, symmetries and the conformal manifold to expectations from six dimensions. These constructions thus give us a detailed understanding of compactifications of two sequences of six dimensional SCFTs to four dimensions. arXiv:1910.03603v1 [hep-th] 8 Oct 2019 7 Discussion 43 A N = 1 superconformal index 44 B Duality proof of symmetry enhancement 46 C Duality proof of exchanging minimal punctures 49

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confidence: 99%

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confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Sequences of 6d SCFTs on generic Riemann surfaces

Razamat

Sabag

2020

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139

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

Buican

Nishinaka

2020

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 ...

An $$ \mathcal{N} $$ = 1 Lagrangian for an $$ \mathcal{N} $$ = 3 SCFT

Zafrir

2021

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We propose that a certain 4d$$ \mathcal{N} $$ N = 1 SU(2) × SU(2) gauge theory flows in the IR to an $$ \mathcal{N} $$ N = 3 SCFT plus a single free chiral field. The specific $$ \mathcal{N} $$ N = 3 SCFT has rank 1 and a dimension three Coulomb branch operator. The flow is generically expected to land at the $$ \mathcal{N} $$ N = 3 SCFT deformed by the marginal deformation associated with said Coulomb branch operator. We also present a discussion about the properties expected of various RG invariant quantities from $$ \mathcal{N} $$ N = 3 superconformal symmetry, and use these to test our proposal. Finally, we discuss a generalization to another $$ \mathcal{N} $$ N = 1 model that we propose is related to a certain rank 3 $$ \mathcal{N} $$ N = 3 SCFT through the turning of certain marginal deformations.