Comments on higher‐spin holography

Bekaert, Xavier; Joung, Euihun; Mourad, J.

doi:10.1002/prop.201200014

Cited by 37 publications

(39 citation statements)

References 35 publications

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“…The Lagrangian of this theory is with interaction (φ i φ i ) 2 , which exists for large N in 4 < d < 6 [2][3][4][5]. The 1/N expansions of various operator scaling dimensions were found in [1] to agree with the corresponding results [6][7][8][9][10][11][12][13][14] in the quartic O(N ) model continued to 6 − dimensions.…”

Section: Introductionsupporting

confidence: 57%

Three loop analysis of the criticalO(N)models in6−εdimensions

et al. 2015

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We continue the study, initiated in arXiv:1404.1094, of the O(N ) symmetric theory of N + 1 massless scalar fields in 6 − dimensions. This theory has cubic interaction terms. We calculate the 3-loop beta functions for the two couplings and use them to determine certain operator scaling dimensions at the IR stable fixed point up to order 3 . We also use the beta functions to determine the corrections to the critical value of N below which there is no fixed point at real couplings. The result suggests a very significant reduction in the critical value as the dimension is decreased to 5. We also study the theory with N = 1, which has a Z 2 symmetry under φ → −φ. We show that it possesses an IR stable fixed point at imaginary couplings which can be reached by flow from a nearby fixed point describing a pair of N = 0 theories. We calculate certain operator scaling dimensions at the IR fixed point of the N = 1 theory and suggest that, upon continuation to two dimensions, it describes a non-unitary conformal minimal model.

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Section: Introductionsupporting

confidence: 57%

Three loop analysis of the criticalO(N)models in6−εdimensions

et al. 2015

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“…The 1/N expansion may be developed in continuous dimension d using a generalized Hubbard-Stratonovich transformation with an auxiliary field σ [16][17][18][19][20][21][22][23][24]. For N ≥ 3, the lower critical dimension is 2, and the perturbative expansions in d = 2 + dimensions may be developed [25] There is an interesting range, 4 < d < 6, where the theory appears to be unitary order by order in the 1/N expansion [27][28][29][30][31]. Yet, the fate of the theory with large but finite N is unclear in view of the expectation, supported by rigorous results [32], that the interacting φ 4 theory cannot exhibit true critical behavior in d > 4.…”

Section: Introductionmentioning

confidence: 99%

O(N) model in 4<d<6 : Instantons and complex CFTs

et al. 2020

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We revisit the scalar O(N ) model in the dimension range 4 < d < 6 and study the effects caused by its metastability. As shown in previous work, this model formally possesses a fixed point where, perturbatively in the 1/N expansion, the operator scaling dimensions are real and above the unitarity bound. Here, we further show that these scaling dimensions do acquire small imaginary parts due to the instanton effects. In d dimensions and for large N , we find that they are of order e −N f (d) , where, remarkably, the function f (d) equals the sphere free energy of a conformal scalar in d − 2 dimensions. The non-perturbatively small imaginary parts also appear in other observables, such as the sphere free energy and two and three-point function coefficients, and we present some of their calculations. Therefore, at sufficiently large N , the O(N ) models in 4 < d < 6 may be thought of as complex CFTs. When N is large enough for the imaginary parts to be numerically negligible, the five-dimensional O(N ) models may be studied using the techniques of numerical bootstrap.Dedicated to the memory of Steve Gubser

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“…At the interacting fixed point, the scaling dimension of the operator φ i φ i is 2 + O(1/N ) for any d. For d > 6, this dimension is below the unitarity bound d/2 − 1. It follows that the interesting range, where the UV fixed point may be unitary, is [20][21][22][23] 4 < d < 6 .…”

Section: Introductionmentioning

confidence: 99%

CriticalO(N)models in6−εdimensions

2014

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We revisit the classic O(N ) symmetric scalar field theories in d dimensions with interaction (φ i φ i ) 2 . For 2 < d < 4 these theories flow to the Wilson-Fisher fixed points for any N . A standard large N Hubbard-Stratonovich approach also indicates that, for 4 < d < 6, these theories possess unitary UV fixed points. We propose their alternate description in terms of a theory of N + 1 massless scalars with the cubic interactions σφ i φ i and σ 3 . Our one-loop calculation in 6 − dimensions shows that this theory has an IR stable fixed point at real values of the coupling constants for N > 1038. We show that the 1/N expansions of various operator scaling dimensions match the known results for the critical O(N ) theory continued to d = 6 − . These results suggest that, for sufficiently large N , there are 5-dimensional unitary O(N ) symmetric interacting CFT's; they should be dual to the Vasiliev higher-spin theory in AdS 6 with alternate boundary conditions for the bulk scalar. Using these CFT's we provide a new test of the 5-dimensional F -theorem, and also find a new counterexample for the C T theorem.

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Comments on higher‐spin holography

Cited by 37 publications

References 35 publications

Three loop analysis of the criticalO(N)models in6−εdimensions

Three loop analysis of the criticalO(N)models in6−εdimensions

O(N) model in 4<d<6 : Instantons and complex CFTs

CriticalO(N)models in6−εdimensions

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