Rationalizing CFTs and anyonic imprints on Higgs branches

We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

Section: Jhep04(2021)076mentioning

confidence: 99%

W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

Xie

Yan

2021

“…We denote this theory by T ( ) n 1 , n 2 , and it has U (n 1 ) × U (1) n 2 −n 1 −2 × U (n 2 ) flavor symmetry. 10 From the quiver diagram, we see that the flavor central charge of the SU (n 1 ) and SU (n 2 ) subgroups are 2n 1 + and 2n 2 − , respectively.…”

Section: More Details Of the Ad Quiver Building Blocksmentioning

confidence: 92%

“…Now we come to the main quiver theories of interest that are built from the above SCFTs and also from fundamental hypermultiplets. To be more explicit, let us take T ( ) n 1 ,n , T ( ) n 2 ,n , 10 Note that, when we write T ( ) n1, n2 , we always have n 1 < n 2 so that (n 2 − n 1 )/ is a positive integer.…”

Section: 2mentioning

confidence: 99%

“…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."…”

mentioning

confidence: 99%

“…• 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].…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Buican

Nishinaka

2020

Self Cite

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 ...

Galois orbits of TQFTs: symmetries and unitarity

Buican

Radhakrishnan

2022

Self Cite

We study Galois actions on 2+1D topological quantum field theories (TQFTs), characterizing their interplay with theory factorization, gauging, the structure of gapped boundaries and dualities, 0-form symmetries, 1-form symmetries, and 2-groups. In order to gain a better physical understanding of Galois actions, we prove sufficient conditions for the preservation of unitarity. We then map out the Galois orbits of various classes of unitary TQFTs. The simplest such orbits are trivial (e.g., as in various theories of physical interest like the Toric Code, Double Semion, and 3-Fermion Model), and we refer to such theories as unitary “Galois fixed point TQFTs”. Starting from these fixed point theories, we study conditions for preservation of Galois invariance under gauging 0-form and 1-form symmetries (as well as under more general anyon condensation). Assuming a conjecture in the literature, we prove that all unitary Galois fixed point TQFTs can be engineered by gauging 0-form symmetries of theories built from Deligne products of certain abelian TQFTs.