Topological correlators and surface defects from equivariant cohomology

Panerai, Rodolfo; Pittelli, Antonio; Polydorou, Konstantina

doi:10.1007/jhep09(2020)185

Cited by 18 publications

(21 citation statements)

References 39 publications

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“…1D topological quantum mechanics) appear as protected subsectors of 4D N = 2 (resp. 3D N = 4) superconformal field theories [8][9][10][11][12][13][14].…”

Section: Jhep08(2021)158mentioning

confidence: 99%

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

Gang

Kim

Lee

et al. 2021

J. High Energ. Phys.

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We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

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“…1D topological quantum mechanics) appear as protected subsectors of 4D N = 2 (resp. 3D N = 4) superconformal field theories [8][9][10][11][12][13][14].…”

Section: Jhep08(2021)158mentioning

confidence: 99%

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

Gang

Kim

Lee

et al. 2021

J. High Energ. Phys.

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“…In well studied cases, e.g., theories of Argyres-Douglas type or class S, much of the recent progress in understanding their chiral algebras has been guided by a set of compelling conjectures [20,21,[40][41][42]. The 3d/1d correspondence is on a somewhat different footing due to the explicit Lagrangians derived in [43][44][45][46]. 2 Nevertheless, applying these results to ABJM theory requires the use of conjectural dualities [49,50] and even then the calculations can be very involved.…”

Section: Jhep04(2021)008mentioning

confidence: 99%

More on holographic correlators: twisted and dimensionally reduced structures

Behan

Ferrero

Zhou

2021

J. High Energ. Phys.

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Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1, 2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For AdS5× S5 and AdS7× S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d $$ \mathcal{N} $$ N = 4 SYM and the 6d (2, 0) theory, finding perfect agreement. For AdS4× S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.

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“…Note that ε 1 is a deformation parameter, and ε 2 is an FI parameter of the 3d N = 4 gauge theory. This 1d TQM was originally studied in [41] using the technique developed in [42](see also [43,44]); a similar discussion using the Coulomb branch algebra [45] can be found in [46].…”

Section: M2 Brane Algebra Amentioning

confidence: 99%