Quartic AdS interactions in higher-spin gravity from Conformal Field Theory

doi:10.1007/JHEP11(2015)149

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Quartic AdS interactions in higher-spin gravity from Conformal Field Theory

Journal Article•DOI•

Quartic AdS interactions in higher-spin gravity from Conformal Field Theory

Xavier Bekaert¹, Johanna Erdmenger², Dmitry Ponomarev³, Charlotte Sleight²•Institutions (3)

François Rabelais University¹, Max Planck Society², Ludwig Maximilian University of Munich³

18 Aug 2015-Journal of High Energy Physics (Springer Berlin Heidelberg)-Vol. 2015, Iss: 11, pp 149

TL;DR: In this paper, the quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of previous results for the Witten diagrams of higher-spin exchanges.

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Abstract: Clarifying the locality properties of higher-spin gravity is a pressing task, but notoriously difficult due to the absence of a weakly-coupled flat regime. The simplest non-trivial case where this question can be addressed is the quartic self-interaction of the AdS scalar field present in the higher-spin multiplet. We investigate this issue in the context of the holographic duality between the minimal bosonic higher-spin theory on AdS4 and the free O(N) vector model in three dimensions. In particular, we determine the exact explicit form of the derivative expansion of the bulk scalar quartic vertex. The quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of our previous results for the Witten diagrams of higher-spin exchanges. This is facilitated by establishing the conformal block expansions of both the boundary four-point function and the dual bulk Witten diagram amplitudes. We show that the vertex we find satisfies a generalised notion of locality.

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Journal Article•DOI•

Higher Spin Interactions from Conformal Field Theory: The Complete Cubic Couplings.

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Charlotte Sleight¹, Massimo Taronna²•Institutions (2)

Max Planck Society¹, Université libre de Bruxelles²

29 Feb 2016-Physical Review Letters

TL;DR: A complete holographic reconstruction of the cubic couplings in the minimal bosonic higher spin theory in (d+1)-dimensional anti- de Sitter space is provided and the operator-product expansion coefficients of all single-trace conserved currents in the d-dimensional free scalar O(N) vector model are determined.

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Abstract: In this Letter we provide a complete holographic reconstruction of the cubic couplings in the minimal bosonic higher spin theory in (d+1)-dimensional anti- de Sitter space. For this purpose, we also determine the operator-product expansion coefficients of all single-trace conserved currents in the d-dimensional free scalar O(N) vector model, and we compute the tree-level three-point Witten diagram amplitudes for a generic cubic interaction of higher spin gauge fields in the metriclike formulation.

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182 citations

Cites background or methods or result from "Quartic AdS interactions in higher-..."

...[13] for any two pairs of spins si set to zero is a nice consistency check....
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...[13] and drawing from the result of Refs....
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...This work constitutes a key step of the holographic reconstruction program, which began with the extraction of the 0-0-s cubic couplings [12–15] and scalar quartic selfinteraction [13,16,17]....
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Journal Article•DOI•

All point correlation functions in SYK

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David J. Gross¹, Vladimir Rosenhaus¹•Institutions (1)

Kavli Institute for Theoretical Physics¹

23 Oct 2017-Journal of High Energy Physics

TL;DR: In this article, it was shown that the three-point function of the primary O(N ) invariant bilinear bilinears fully determines all correlation functions, to leading nontrivial order in 1/N, through simple Feynman-like rules.

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Abstract: Large N melonic theories are characterized by two-point function Feynman diagrams built exclusively out of melons. This leads to conformal invariance at strong coupling, four-point function diagrams that are exclusively ladders, and higher-point functions that are built out of four-point functions joined together. We uncover an incredibly useful property of these theories: the six-point function, or equivalently, the three-point function of the primary O(N ) invariant bilinears, regarded as an analytic function of the operator dimensions, fully determines all correlation functions, to leading nontrivial order in 1/N , through simple Feynman-like rules. The result is applicable to any theory, not necessarily melonic, in which higher-point correlators are built out of four-point functions. We explicitly calculate the bilinear three-point function for q-body SYK, at any q. This leads to the bilinear four-point function, as well as all higher-point functions, expressed in terms of higher-point conformal blocks, which we discuss. We find universality of correlators of operators of large dimension, which we simplify through a saddle point analysis. We comment on the implications for the AdS dual of SYK.

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165 citations

Journal Article•DOI•

Light-front higher-spin theories in flat space

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Dmitry Ponomarev¹, Evgeny Skvortsov²•Institutions (2)

Imperial College London¹, Ludwig Maximilian University of Munich²

25 Jan 2017-Journal of Physics A

TL;DR: In this article, it was shown that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approach.

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Abstract: We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields-the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local.

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159 citations

Cites background from "Quartic AdS interactions in higher-..."

...Aiming at the unitary and parity preserving higher-spin theory in flat space we reconstruct the part of the quartic Hamiltonian that contains self-interactions of the scalar field, which can be regarded as the flat space counterpart of the AdS4 result [37, 38]....
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...This can be thought of as the Minkowski space counterpart of the AdS result obtained recently in [37, 38]....
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Journal Article•DOI•

A Mellin space approach to cosmological correlators

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Charlotte Sleight¹, Charlotte Sleight²•Institutions (2)

Université libre de Bruxelles¹, Institute for Advanced Study²

01 Jan 2020-Journal of High Energy Physics

TL;DR: In this article, the Mellin-Barnes representation is used for the evaluation of late-time momentum-space correlation functions of quantum fields in (d + 1)-dimensional de Sitter space.

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Abstract: We propose a Mellin space approach to the evaluation of late-time momentum-space correlation functions of quantum fields in (d + 1)-dimensional de Sitter space. The Mellin-Barnes representation makes manifest the analytic structure of late-time correlators and, more generally, provides a convenient general d framework for the study of conformal correlators in momentum space. In this work we focus on tree-level correlation functions of general scalars as a prototype, including n-point contact diagrams and 4-point exchanges. For generic scalars, both the contact and exchange diagrams are given by (generalised) Hypergeometric functions, which reduce to existing expressions available in the literature for d = 3 and external scalars which are either simultaneously conformally coupled or massless. This approach can also be used for the perturbative bulk evaluation of momentum space boundary correlators in (d + 1)-dimensional anti-de Sitter space (Witten diagrams).

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152 citations

Journal Article•DOI•

Higher-Spin Gauge Theories and Bulk Locality

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Charlotte Sleight¹, Massimo Taronna¹•Institutions (1)

Université libre de Bruxelles¹

26 Oct 2018-Physical Review Letters

TL;DR: The result suggests that the Fronsdal program for introducing interactions among higher-spin gauge fields cannot be completed without introducing new guiding principles, which could potentially lie beyond the framework of classical field theory.

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Abstract: We present a no-go result on consistent Noether interactions among higher-spin gauge fields on anti--de Sitter space-times. We show that there is a nonlocal obstruction at the classical level to consistent interacting field theory descriptions of massless higher-spin particles that are described in the free limit by the free Fronsdal action, under the assumption that such theories arise from the gauging of a global higher-spin symmetry. Our result suggests that the Fronsdal program for introducing interactions among higher-spin gauge fields cannot be completed without introducing new guiding principles, which could potentially lie beyond the framework of classical field theory.

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127 citations

Cites background or methods or result from "Quartic AdS interactions in higher-..."

...38) for the correlator is shown in reference [95], section 5....
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...20 For example, the quartic self-interaction of the scalar φ0 is expected to have a derivative expansion of the form [95]...
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...40) was computed for any s in [94] (see the earlier [95, 119] for the 0-0-0-0 case)....
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...To conclude this subsection we briefly compare our results to those in an earlier work [95], which carried out a similar investigation on the locality of the quartic scalar self-interaction in the minimal higher-spin theory....
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...One chooses a = 0 and c = 1 in the function defined in [95] which is labelled by the symbol F ....
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References

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Journal Article•DOI•

AdS dual of the critical O(N) vector model

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Igor R. Klebanov¹, Alexander M. Polyakov¹•Institutions (1)

Princeton University¹

19 Dec 2002-Physics Letters B

TL;DR: In this article, a general relation between theories of infinite number of higher-spin massless gauge fields in AdS d + 1 and large N conformal theories in d dimensions containing N -component vector fields was proposed.

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1,260 citations

"Quartic AdS interactions in higher-..." refers background in this paper

...A decade ago, it was conjectured [38,39] that unbroken Vasiliev’s higher-spin theory [40–42] is dual to the free O(N) vector model....
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Journal Article•DOI•

Holography from Conformal Field Theory

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Idse Heemskerk¹, Joao Penedones², Joseph Polchinski², James Sully¹•Institutions (2)

University of California, Santa Barbara¹, Kavli Institute for Theoretical Physics²

27 Oct 2009-Journal of High Energy Physics

TL;DR: In this paper, it was shown that any CFT with a large-N expansion and a large gap has a local bulk dual, and that the conjecture is true in a broad range of CFT's, to first nontrivial order in 1/N-2.

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Abstract: The locality of bulk physics at distances below the AdS length scale is one of the remarkable aspects of AdS/CFT duality, and one of the least tested. It requires that the AdS radius be large compared to the Planck length and the string length. In the CFT this implies a large-N expansion and a gap in the spectum of anomalous dimensions. We conjecture that the implication also runs in the other direction, so that any CFT with a large-N expansion and a large gap has a local bulk dual. For an abstract CFT we formulate the consistency conditions, most notably crossing symmetry, and show that the conjecture is true in a broad range of CFT's, to first nontrivial order in 1/N-2: in any CFT with a gap and a large-N expansion, the four-point correlator is generated via the AdS/CFT dictionary from a local bulk interaction. We establish this result by a counting argument on each side, and also investigate various properties of some explicit solutions.

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947 citations

"Quartic AdS interactions in higher-..." refers background or result in this paper

...The latter is only known in d = 4 CFTs [76] in the literature, whereas for the former only partial results are known in certain limits [62]....
[...]
...This result is consistent with observations in the literature [62, 95] for lower-spin exchanges, that an exchange Witten diagram does not simply correspond in the CFT to the exchange of the operator dual to the exchanged bulk field: There are additional contributions from doubletrace operators built from the single-trace operators that are dual to the external fields of the exchange Witten diagram....
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...A similar analysis can be found in [62], where...
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...Independent flat space 4-point amplitudes have been counted in [62]....
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...the coefficients in the derivative expansion of the vertex [62], and ensures that it is weakly local....
[...]

Journal Article•DOI•

Massless Fields with Integer Spin

[...]

Christian Fronsdal¹•Institutions (1)

University of California, Los Angeles¹

15 Nov 1978-Physical Review D

TL;DR: In this paper, the Fierz-Pauli Lagrangian for massive particles with arbitrary integral spin $s, first obtained by Hagen and Singh, is examined in the limit of vanishing mass.

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Abstract: The Fierz-Pauli Lagrangian for massive particles with arbitrary integral spin $s$, first obtained by Hagen and Singh, is examined in the limit of vanishing mass. Unexpectedly, a considerable simplification occurs. The potential $h$ is a symmetric tensor of rank $s$; the "trace" ${h}^{\ensuremath{'}}$, obtained by contraction of a pair of indices against the flat-space metric, does not vanish but the trace ${h}^{\ensuremath{'}\ensuremath{'}}$ of ${h}^{\ensuremath{'}}$ does. The wave equation admits a gauge group, and this implies conditions on the source. The divergence of the source need not vanish, only the traceless projection of the divergence must be zero; this is a major departure from the usual assumption and may bear on the question of the existence of a physically interesting source for fields with spin \ensuremath{\ge}3. This weaker condition on the source is sufficient to guarantee that only $\mathrm{helicities}\ifmmode\pm\else\textpm\fi{}s$ are transmitted between sources. A generalized Gupta program is proposed, that is, a search for a scheme for generating a theory of interacting, massless particles, consistent to all orders in the coupling constant.

...read moreread less

864 citations

"Quartic AdS interactions in higher-..." refers background in this paper

...This spectacular property was expected since the formulation of the higher-spin interaction problem [27] and comes from the structure of the higher-spin algebra, which is to large extent unique [28, 29]....
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Journal Article•DOI•

Conformal four point functions and the operator product expansion

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F.A. Dolan, Hugh Osborn

02 Apr 2001-Nuclear Physics

TL;DR: In this paper, a recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function for scalar fields in conformally invariant theories is derived.

...read moreread less

844 citations

"Quartic AdS interactions in higher-..." refers background or result in this paper

...The latter is only known in d = 4 CFTs [76] in the literature, whereas for the former only partial results are known in certain limits [62]....
[...]
...This requires the knowledge of the OPE coefficients of the operators in the scalar singlet OPE, which for the double-trace operators were so far absent in the literature – with the exception of the d = 4 case derived in [76]....
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...For the double-trace operators O((2)) n,s, so far the OPE coefficients have been determined only for d = 4 in [76]....
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...This agrees with the result of [76] for d = 4 and ∆ = 2, as does the analogous calculation of the OPE coefficients for s fixed and n = 0, 1....
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...We also comment on the role of holography in the locality of interactions in higher-spin theory duals to CFTs....
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Journal Article•DOI•

Nonlinear equations for symmetric massless higher spin fields in (A)dSd

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Mikhail A. Vasiliev¹•Institutions (1)

Lebedev Physical Institute¹

07 Aug 2003-Physics Letters B

TL;DR: In this article, nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented, and a nonlinear nonlinear model of the field equations is proposed.

...read moreread less

756 citations