(2,0) Superconformal OPE's in <i>D</i> = 6, selection rules and non-renormalization theorems

Eden, Burkhard; Sokatchev, E.; Ferrara, S.

doi:10.1088/1126-6708/2001/11/020

Cited by 27 publications

(69 citation statements)

References 33 publications

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“…It is equivalent but technically simpler to focus on the four-point function of Φ, which contains the same information as the stress tensor four-point function. (Indeed, the two-, three-and four-point functions of all half BPS multiplets are known to admit a unique structure in superspace [47][48][49]. )…”

Section: B Bootstrap Approachmentioning

confidence: 99%

“…Building on previous work [47][48][49]53,54], we impose the constraints of superconformal invariance on the fourpoint function of Φ and decompose it in a double OPE expansion into an infinite sum of superconformal blocks. Schematically we have…”

Section: B Bootstrap Approachmentioning

confidence: 99%

“…For some special cases the selection rules have been determined explicitly; cf. [47,48,53,54]. We will use a particular case of this below in our discussion of half BPS operators.…”

Section: Selection Rulesmentioning

confidence: 99%

“…It is a convenient fact that the full superspace structure of a three-point function involving two half BPS multiplets and any third multiplet is completely determined by the three-point function of superconformal primary operators [47]. Since the superconformal primaries of half BPS representations are spacetime scalars, it follows that each such superspace three-point function is determined by a single numerical coefficient.…”

Section: Three-point Functionsmentioning

confidence: 99%

“…For the particular case of the OPE of two half BPS operators, these selection rules have been studied starting with the work of [47,48,53], with the complete answer being given in [54]. The results are as follows:…”

Section: Selection Rulesmentioning

confidence: 99%

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The (2, 0) superconformal bootstrap

et al. 2016

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We develop the conformal bootstrap program for six-dimensional conformal field theories with (2, 0) supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on operator product expansion (OPE) coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the light cone expansion of the crossing equation. Our principal result is strong evidence that the A 1 theory realizes the minimal allowed central charge (c ¼ 25) for any interacting (2, 0) theory. This implies that the full stress tensor four-point function of the A 1 theory is the unique unitary solution to the crossing symmetry equation at c ¼ 25. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting (2, 0) theory of central charge c. For large c, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

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Section: B Bootstrap Approachmentioning

confidence: 99%

Section: B Bootstrap Approachmentioning

confidence: 99%

“…For some special cases the selection rules have been determined explicitly; cf. [47,48,53,54]. We will use a particular case of this below in our discussion of half BPS operators.…”

Section: Selection Rulesmentioning

confidence: 99%

Section: Three-point Functionsmentioning

confidence: 99%

Section: Selection Rulesmentioning

confidence: 99%

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The (2, 0) superconformal bootstrap

et al. 2016

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Regge trajectories for the (2, 0) theories

Lemos

Rees

Zhao

2022

J. High Energ. Phys.

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We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2, 0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge trajectories. We show that these super-descendant trajectories interact in interesting ways, leading to new constraints on their shape. For the four-point function of the stress tensor multiplet supersymmetry also softens the Regge behavior in some channels, and consequently we observe that ‘analyticity in spin’ holds for all spins greater than −3. All the physical operators in this correlator therefore lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function. Some numerical experiments yield promising results, with OPE data approaching the numerical bootstrap results for all theories with rank greater than one.

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M-theory beyond the supergravity approximation

Heslop

Lipstein

2018

J. High Energ. Phys.

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Abstract:We analyze the four-point function of stress-tensor multiplets for the 6d quantum field theory with OSp(8 * |4) symmetry which is conjectured to be dual to M-theory on AdS 7 × S 4 , and deduce the leading correction to the tree-level supergravity prediction by obtaining a solution of the crossing equations in the large-N limit with the superconformal partial wave expansion truncated to operators with zero spin. This correction corresponds to the M-theoretic analogue of R 4 corrections in string theory. We also find solutions corresponding to higher-spin truncations, but they are subleading compared to the 1-loop supergravity prediction, which has yet to be calculated.

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(2,0) Superconformal OPE's in D = 6, selection rules and non-renormalization theorems

Cited by 27 publications

References 33 publications

The (2, 0) superconformal bootstrap

The (2, 0) superconformal bootstrap

Regge trajectories for the (2, 0) theories

M-theory beyond the supergravity approximation

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