Supersymmetric dS/CFT

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 ...

Section: Wave Function Relations and Topology Of 3d Mirrorsmentioning

confidence: 98%

Section: Wave Function Relations and Topology Of 3d Mirrorsmentioning

confidence: 99%

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

Buican

Nishinaka

2020

“…For further developments in this direction, see [6][7][8][9][10][11][12]. These studies mostly exploit the higher spin symmetries.…”

Section: Jhep03(2018)153mentioning

confidence: 99%

“…According to these proposals, the rigid symmetries of the vacuum should leave the extensive variables invariant while acting nontrivially on the microscopic variables; for related remarks, see [18,46]. 10 The full field configurations are thus assumed to contain contain asymptotically (anti-)de Sitter regions where the full tensor gauge fields φ a(s) approach Fronsdal fields give on shell in terms of polarization tensors that are non-linear functionals of the zero-form initial data C.…”

Section: Gauge Functionsmentioning

confidence: 99%

FRW and domain walls in higher spin gravity

Aros

Iazeolla

Noreña

et al. 2018

We present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in spacetime, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in (A)dS 4 . We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.

“…[23][24][25]) because in dS space there is no positive conserved quantity whereas supersymmetry would allow one to construct one. However supersymmetric HS gravity theories in de Sitter circumvent this problem since the Hermitian conjugate in the theories in [26] is an anti-involution [22]. In a similar spirit one may object that de Sitter space 'has a temperature' and therefore cannot be supersymmetric.…”

mentioning

confidence: 99%

Spinors in supersymmetric dS/CFT

Hertog

Tartaglino‐Mazzucchelli

Venken

2019

Self Cite

We study fermionic bulk fields in the dS/CFT dualities relating N = 2 supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to supersymmetric Vasiliev theories in fourdimensional de Sitter space. These dualities specify the Hartle -Hawking wave function in terms of the partition function of deformations of the vector models. We evaluate this wave function in homogeneous minisuperspace models consisting of supersymmetry-breaking combinations of a half-integer spin field with either a scalar, a pseudoscalar or a metric squashing. The wave function appears to be well-behaved and globally peaked at or near the supersymmetric de Sitter vacuum, with a low amplitude for large deformations. Its behavior in the semiclassical limit qualitatively agrees with earlier bulk computations both for massless and massive fermionic fields. * Electronic address: thomas.hertog@kuleuven.be † Electronic address: gtm@itp.unibe.ch ‡ Electronic address: gerben.venken@kuleuven.be