Spinning conformal blocks

Costa, Miguel S.; Penedones, João; Poland, David; Rychkov, Slava

doi:10.1007/jhep11(2011)154

Cited by 292 publications

(605 citation statements)

References 54 publications

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“…Since in d = 3 dimensions the only possible operators are traceless symmetric tensors with indexes the number of unrestricted degrees of freedom governing a correlator of four conserved currents is given by n 2 where n is a number of three-point functions JJO µ 1 ...µ . This number was found in [30] to be 4. Hence there are 4 2 = 16 functional degrees of freedom governing JJJJ in d = 3.…”

Section: B Conformal Block Decomposition In D =mentioning

confidence: 84%

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

Dymarsky

2015

J. High Energ. Phys.

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Abstract:We discuss to what extent the full set of Ward Identities constrain the fourpoint function of the stress-energy tensors or conserved currents in a conformal field theory. We calculate the number of kinematically unrestricted functional degrees of freedom governing the corresponding correlators and find that it matches the number of functional degrees of freedom governing scattering amplitudes of some "dual" massless particles in the auxiliary Minkowski space. We also formulate the conformal bootstrap constraints for the correlators in question in terms of only unrestricted degrees of freedom. As a byproduct we find interesting parallels between solving Ward Identities in coordinate and momentum space.

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Section: B Conformal Block Decomposition In D =mentioning

confidence: 84%

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

Dymarsky

2015

J. High Energ. Phys.

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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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“…The embedding formalism [33][34][35][36][37][38][39] realizes conformal transformations linearly and provides a convenient way to construct conformally covariant correlation functions. Specifically, the conformal covariance of correlation function is mapped into the Lorentz covariance of the correlation function in embedding space.…”

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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Spinning conformal blocks

Cited by 292 publications

References 54 publications

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

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

The (2, 0) superconformal bootstrap

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

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