General three-point functions in 4D CFT

Elkhidir, Emtinan; Karateev, Denis; Serone, Marco

doi:10.1007/jhep01(2015)133

Cited by 65 publications

(111 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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“…8 Our first task is to explicitly construct the three-point function T hh † including the constraints of conservation of T and the conformal Ward identities. We do this explicitly in appendix B.1 for k ≤ 7 following the method of [18] by systematically constructing all possible conformal invariants of the correct scaling and imposing the derivative and integral constraints. Our results are given in tables 2-5 of appendix B.2.2.…”

Section: Jhep02(2018)131 3 Constraining Operators In (K 1) Representmentioning

confidence: 99%

“…If one wanted to study correlation functions that did not have this property, however, one would need to account for tensor structures that involve K orK tensors. 11 Relative to [18], we have defined the Iij and Ji tensors to be the values one obtains after projection from six to four dimensions instead of the six-dimensional expression. Also, we have added a minus sign to Iij for i < j to simplify OPE limit expressions.…”

Section: B11 Conformal Building Blocks For Three-point Functionsmentioning

confidence: 99%

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Universal bounds on operator dimensions from the average null energy condition

Córdova

Diab

2018

J. High Energ. Phys.

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We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highly-chiral primary operators in four-dimensional conformal field theories. Denoting the spin of an operator by a pair of integers (k,k) specifying the transformations under chiral su(2) rotations, we explicitly demonstrate these new bounds for operators transforming in (k, 0) and (k, 1) representations for sufficiently large k. Based on these calculations, along with intuition from free field theory, we conjecture that in any unitary conformal field theory, primary local operators of spin (k,k) and scaling dimension ∆ satisfy ∆ ≥ max{k,k}. If |k −k| > 4, this is stronger than the unitarity bound.

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“…Specifically, the conformal covariance of correlation function is mapped into the Lorentz covariance of the correlation function in embedding space. Recently, the embedding formalism has been widely used to study the conformal blocks of spinor and tensor operators [21,25,[40][41][42][43][44]. The SU(2, 2|N ) superconformal symmetry transformations can be linearly realized in the supersymmetric generalizationsuperembedding space [45][46][47][48][49].…”

Section: Jhep05(2016)163mentioning

confidence: 99%

The most general 4 D $$ \mathcal{D} $$ N $$ \mathcal{N} $$ = 1 superconformal blocks for scalar operators

2016

J. High Energ. Phys.

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We compute the most general superconformal blocks for scalar operators in 4D N = 1 superconformal field theories. Specifically we employ the supershadow formalism to study the four-point correlator Φ 1 Φ 2 Φ 3 Φ 4 , in which the four scalars, Φ i , have arbitrary scaling dimensions and R-charges. The only constraint on the R-charges is from R-symmetry invariance of the four-point correlator and the exchanged operators can have arbitrary R-charges. Our results extend previous studies on 4D N = 1 superconformal blocks to the most general case, which are the essential ingredient for bootstrapping mixed correlators of scalars with independent scaling dimensions and R-charges.

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General three-point functions in 4D CFT

Cited by 65 publications

References 36 publications

The (2, 0) superconformal bootstrap

The (2, 0) superconformal bootstrap

Universal bounds on operator dimensions from the average null energy condition

The most general 4 D $$ \mathcal{D} $$ N $$ \mathcal{N} $$ = 1 superconformal blocks for scalar operators

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