On the proposed AdS dual of the critical O(N) sigma model for any dimension 2&lt;d&lt;4

Leonhardt, Thorsten; Meziane, A.; Rühl, W.

doi:10.1016/s0370-2693(03)00058-3

Cited by 29 publications

(25 citation statements)

References 19 publications

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“…The coefficients c 2 ) have even a double zero from the Γ(2µ − 3) −2 , but this zero is compensated by a double pole for all but a few (n, m). These surviving terms lead to current exchanges, as discussed in [20]. We shall return to them below.…”

Section: The O(n ) Model At Its Interacting Fixed Pointmentioning

confidence: 95%

The minimal conformalO(N) vector sigma model atd= 3

Leonhardt¹,

Rühl²

2004

J. Phys. A: Math. Gen.

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For the minimal O(N) sigma model, which is defined to be generated by the O(N) scalar auxiliary field alone, all n-point functions, till order 1/N included, can be expressed by elementary functions without logarithms. Consequently, the conformal composite fields of m auxiliary fields possess at the same order such dimensions, which are m times the dimension of the auxiliary field plus the order of differentiation.

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Section: The O(n ) Model At Its Interacting Fixed Pointmentioning

confidence: 95%

The minimal conformalO(N) vector sigma model atd= 3

Leonhardt¹,

Rühl²

2004

J. Phys. A: Math. Gen.

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“…The exact summation of the corresponding exchange amplitudes for an infinite tower of intermediate tensor gauge fields is possible in flat spacetime [6] and one might hope to reproduce the analogue of this result in AdS d since all ingredients are now available in the unconstrained formalism for irreducible gauge fields: the bulk-to-bulk propagators of symmetric tensor fields can be extracted from [24] and the relevant cubic vertices have been presented here. 3 Moreover, the CF T d−1 dual results are known in closed form, even for the interacting O(N ) model in the large N limit [56]. Computing explicitly the AdS d exchange Witten diagram could therefore provide a first quantitative test of the AdS 4 /CF T 3 conjecture of Klebanov and Polyakov [55] at quartic level, i.e.…”

Section: Jhep11(2010)116mentioning

confidence: 98%

Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

Bekaert

Meunier

2010

J. High Energ. Phys.

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Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated on any constant curvature spacetime of dimension d 3. Following Noether's method, the gauge fields interact with the scalar field via minimal coupling to the conserved currents. A symmetric conserved current, bilinear in the scalar field and containing up to r derivatives, is obtained for any rank r 1 from its flat spacetime counterpart in dimension d + 1, via a radial dimensional reduction valid precisely for the mass-square domain of unitarity in (anti) de Sitter spacetime of dimension d. The infinite collection of conserved currents and cubic vertices are summarized in a compact form by making use of generating functions and of the Weyl/Wigner quantization on constant curvature spaces.

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“…[27][28][29] for recent results. Bulk locality of 12 See for example [81,82], and the ensuing discussions. 13 The relevance of such terms was already emphasised in [87] in the particular case of the "Born-Infeld tail".14 All results can be Wick-rotated to Minkowski signature, with careful treatment of the i prescription.…”

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confidence: 99%

Towards holographic higher-spin interactions: four-point functions and higher-spin exchange

Bekaert

Erdmenger

Ponomarev³

et al. 2015

J. High Energ. Phys.

100

168

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Within holography, we calculate the contribution of an arbitrary spin-s gauge boson exchange in AdS d+1 to the four-point function with scalar operators on the boundary. As an important ingredient, we first compute the complete bulk-to-bulk propagators for massless bosonic higher-spin fields in the metric-like formulation, in any dimension and in various gauges. The split representation of the bulk-to-bulk propagators in terms of bulk-to-boundary propagators allows to present the higher-spin exchange diagram in the form of a conformal partial wave expansion. Our results provide a step towards the larger goal of the holographic reconstruction of bulk interactions, and of clarifying bulk locality.

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On the proposed AdS dual of the critical O(N) sigma model for any dimension 2<d<4

Cited by 29 publications

References 19 publications

The minimal conformalO(N) vector sigma model atd= 3

The minimal conformalO(N) vector sigma model atd= 3

Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

Towards holographic higher-spin interactions: four-point functions and higher-spin exchange

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