Sphere correlation functions and Verma modules

Gaiotto, Davide; Okazaki, Tadashi

doi:10.1007/jhep02(2020)133

Cited by 30 publications

(57 citation statements)

References 70 publications

(101 reference statements)

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“…The most glaring aspect of twisted holography 4 is an correspondence between operator algebra in both sides, which is manifested by a rigorous Koszul duality. Moreover, the information of physical observables such as Witten diagrams in the bulk side that match with correlation functions in the boundary side is fully captured by OPE algebra in the twisted sector [37].…”

Section: Twisted Holography Via Koszul Dualitymentioning

confidence: 99%

Feynman diagrams and $Ω$-deformed M-theory

Zhou

2021

SciPost Phys.

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Section: Twisted Holography Via Koszul Dualitymentioning

confidence: 99%

Feynman diagrams and $Ω$-deformed M-theory

Zhou

2021

SciPost Phys.

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“…in the chiral ring. 3939 This conclusion also holds for n = 4, from squaring both sides of(Q 1 ) i (Q 1 ) j + (Q 3 ) i (Q 3 ) j = −(Q 2 ) i (Q 2 ) j − (Q 4 ) i (Q 4 ) j .…”

mentioning

confidence: 79%

“…See[39] for a complementary perspective on these protected correlation functions 5. Mixed-branch operators are not in the cohomology of either supercharge.…”

mentioning

confidence: 99%

Non-Abelian mirror symmetry beyond the chiral ring

Fan

Wang

2020

Phys. Rev. D

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Mirror symmetry is a type of infrared duality in 3D quantum field theory that relates the low-energy dynamics of two distinct ultraviolet descriptions. Though first discovered in the supersymmetric context, it has far-reaching implications for understanding nonperturbative physics in general 3D quantum field theories. We study mirror symmetry in 3D N = 4 supersymmetric field theories whose Higgs or Coulomb branches realize D-and E-type Kleinian singularities in the ADE classification, generalizing previous work on the A-type case. Such theories include the SU (2) gauge theory coupled to fundamental matter in the D-type case and non-Lagrangian generalizations thereof in the E-type case. In these cases, the mirror description is given by a quiver gauge theory of affine D-or E-type. We investigate the mirror map at the level of the recently identified 1D protected subsector described by topological quantum mechanics, which implements a deformation quantization of the corresponding ADE singularity. We give an explicit dictionary between the monopole operators and their dual mesonic operators in the D-type case. Along the way, we extract various operator product expansion (OPE) coefficients for the quantized Higgs and Coulomb branches. We conclude by offering some perspectives on how the topological subsectors of the E-type quivers might shed light on their non-Lagrangian duals.2 A variation of the Ω-background [25][26][27] leads to related deformation quantizations of the Higgs and Coulomb branches [28][29][30]. It would be interesting to spell out the explicit relation to the TQM sector.3 Specifically, the abelian A-type mirror symmetries were analyzed in [32], and a simple N = 8 nonabelian A-type mirror symmetry was analyzed in [33]. The D 3 case was also discussed in Appendix F.2 of [33], but this belongs to the A-series (D 3 ∼ = A 3 ).

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“…The same approach was later extended to the Coulomb-branch sector through mirror symmetry [6,7], and to five dimensions [8]. For other recent developments, see also [9][10][11].…”

Section: Jhep09(2020)185mentioning

confidence: 99%

“…for −2π < t < 2π, with t = t 2 − t 1 . For values of t outside of this domain, G + and G − should be defined by simply enforcing the periodicity condition 11) which is manifest in (5.8).…”

Section: Jhep09(2020)185mentioning

confidence: 99%

Topological correlators and surface defects from equivariant cohomology

Panerai

Pittelli

Polydorou

2020

J. High Energ. Phys.

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We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

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Sphere correlation functions and Verma modules

Abstract: We propose a universal IR formula for the protected three-sphere correlation functions of Higgs and Coulomb branch operators of N = 4 supersymmetric quantum field theories with massive, topologically trivial vacua.7 Also see [4][5][6].

Cited by 30 publications

References 70 publications

Feynman diagrams and $Ω$-deformed M-theory

Feynman diagrams and $Ω$-deformed M-theory

Non-Abelian mirror symmetry beyond the chiral ring

Topological correlators and surface defects from equivariant cohomology

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