Conformal correlators of mixed-symmetry tensors

We classify and compute, by means of the six-dimensional embedding formalism in twistor space, all possible three-point functions in four dimensional conformal field theories involving bosonic or fermionic operators in irreducible representations of the Lorentz group. We show how to impose in this formalism constraints due to conservation of bosonic or fermionic currents. The number of independent tensor structures appearing in any three-point function is obtained by a simple counting. Using the Operator Product Expansion (OPE), we can then determine the number of structures appearing in 4-point functions with arbitrary operators. This procedure is independent of the way we take the OPE between pairs of operators, namely it is consistent with crossing symmetry, as it should be. An analytic formula for the number of tensor structures for three-point correlators with two symmetric and an arbitrary bosonic (non-conserved) operators is found, which in turn allows to analytically determine the number of structures in 4-point functions of symmetric traceless tensors.

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“…During the final stages of this work, ref. [14] appeared, where tensors with mixed symmetry are studied. Ref.…”

Section: Discussionmentioning

confidence: 99%

“…Ref. [14] considers CFTs in arbitrary dimensions, but focuses on bosonic, non-conserved, operators only. When a comparison is possible, the number of tensor structures computed in the examples considered in ref.…”

Section: Discussionmentioning

confidence: 99%

General three-point functions in 4D CFT

Elkhidir

Karateev

Serone

2015

J. High Energ. Phys.

101

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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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“…However, the class of conformal blocks derived in this way is associated to the exchange of traceless symmetric operators O, whereas tensor correlator bootstrap requires, in addition, the exchange of mixed-symmetric operators A. Later, in [45,46] it was shown that conformal blocks associated to A can be calculated as a (finite) sum of scalar blocks evaluated at zero spin which, in principle, can be done by a computer. However, the numerical evaluation of these blocks is quite resource intensive due to the fact that the number of terms in the sum increases rapidly with the spin of A.…”

Section: Jhep01(2016)139mentioning

confidence: 99%

“…There is a large body of work on irreducible representations of SO(D) (for instance see the nice discussion in [46] and references therein), but we really don't need the full power of this theory for the current work. Consider a tensor with n indices.…”

Section: A Building Blocks and Identitiesmentioning

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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Conformal correlators of mixed-symmetry tensors

Cited by 112 publications

References 57 publications

General three-point functions in 4D CFT

General three-point functions in 4D CFT

The (2, 0) superconformal bootstrap

Scalar-vector bootstrap

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