On the four-point function of the stress-energy tensors in a CFT

Dymarsky, Anatoly

doi:10.1007/jhep10(2015)075

Cited by 45 publications

(78 citation statements)

References 36 publications

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“…16 In fact, the technology to bootstrap four-point functions involving external tensorial operators, while conceptually straightforward, has not yet been fully developed. Rapid progress is being made in the area-see [103][104][105][106][107][108][109][110][111][112][113][114][115][116][117].…”

Section: A Structure Of the Four-point Functionmentioning

confidence: 99%

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: A Structure Of the Four-point Functionmentioning

confidence: 99%

The (2, 0) superconformal bootstrap

et al. 2016

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“…stress-energy tensors). Finally, the most ambitious goal would be to bootstrap the four-point function of conserved stress-tensors (see for example the discussion in [50]). This is probably not feasible using our current techniques "by hand", but might be possible if we can computerize the necessary steps.…”

Section: Jhep01(2016)139mentioning

confidence: 99%

Scalar-vector bootstrap

Rejón-Barrera

Robbins

2016

J. High Energ. Phys.

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Abstract:We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.

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“…[44,45] for important early works on tensor correlators and refs. [8,9,19,[46][47][48][49][50][51] for other recent studies) using the 6D embedding formalism [52][53][54][55] formulated in terms of twistors in an index-free notation [11] (see e.g. refs.…”

Section: Three-point Function Classificationmentioning

confidence: 99%

“…For four identical conserved currents, N 4 = 7 + , as indicated in table 1, and agrees with what found in ref. [49].…”

Section: Spin 1 Four-point Functionsmentioning

confidence: 99%

Deconstructing conformal blocks in 4D CFT

Echeverri

Elkhidir

Karateev

et al. 2015

J. High Energ. Phys.

119

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We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential operators for all possible conformal partial waves associated to four-point functions of arbitrary traceless symmetric operators. Our method allows any conformal partial wave to be extracted from a few "seed" correlators, simplifying dramatically the computation needed to bootstrap tensor correlators.

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On the four-point function of the stress-energy tensors in a CFT

Cited by 45 publications

References 36 publications

The (2, 0) superconformal bootstrap

The (2, 0) superconformal bootstrap

Scalar-vector bootstrap

Deconstructing conformal blocks in 4D CFT

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