On the Weyl anomaly of 4D conformal higher spins: a holographic approach

Acevedo, S.; Aros, Rodrigo; Bugini, F.; Díaz, D. E.

doi:10.1007/jhep11(2017)082

Cited by 9 publications

(20 citation statements)

References 92 publications

(126 reference statements)

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“…This shortcut route to the Weyl anomaly has already been noticed in[39] and successfully put into use by[40,35,36].3 A 9 is equivalent to −A 5 , up to a trivial total derivative 4. We notice a misprint in the coefficient of A 13 for the scalar in[13], but fortunately it does not alter the subsequent results therein.…”

supporting

confidence: 54%

“…To close, let us mention two further directions in which we envisage extensions of our present calculations to higher-derivative operators: one is related to the family of GJMS-like two-tensor operators of [12]; and the second also starts with the 6D Weyl graviton, but this time it goes higher in spin, i.e., the extension to 6D Conformal Higher Spins [54,35].…”

Section: Resultsmentioning

confidence: 99%

“…In any case, an interesting interplay between boundary factorization 10 This "accidental" equalities have previously been noticed for the case of higher spin fields in 5D/4D (cf. [35], footnote 8 therein).…”

Section: Miscellany: Boundary Factorization Vs Bulk Wkb Exactnessmentioning

confidence: 99%

“…Most of the traces are easily related to the quadratic ones already computed in [35]. As for the challenging ones, those ofV 4 ,V 11 andV 12 , we used the CADABRA code [49,50] to implement and compute them.…”

Section: Non-conformally Flat Case: Poincaré-einstein Metricmentioning

confidence: 99%

“…The precise correspondence between one-loop partition functions for the 5D Einstein graviton and 4D Weyl graviton has already been established: although the one-loop divergences of 4D Weyl gravity have long been known [37,38], the bulk counterpart has recently been given a successful treatment [35]. In turn, the 7D holographic counterpart, to date, only accounts for the type-A anomaly coefficient by explicit evaluation of the corresponding functional determinants on hyperbolic space [14].…”

Section: Introductionmentioning

confidence: 99%

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One-loop divergences in 7D Einstein and 6D conformal gravities

Aros

Bugini

Díaz

2020

J. High Energ. Phys.

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The aim of this note is to unveil a striking equivalence between the one-loop divergences in 7D Einstein and 6D Conformal Gravities. The particular combination of 6D pointwise Weyl invariants of the 6D Conformal Gravity corresponds to that of Branson's Q-curvature and can be written solely in terms of the Ricci tensor and its covariant derivatives. The quadratic metric fluctuations of this action, 6D Weyl graviton, are endowed with a sixthorder kinetic operator that happens to factorize on a 6D Einstein background into product of three shifted Lichnerowicz Laplacians. We exploit this feature to use standard heat kernel techniques and work out in one go the UV logarithmic divergences of the theory that contains in this case the four Weyl anomaly coefficients. In a seemingly unrelated computation, we determine the one-loop IR logarithmic divergences of 7D Einstein Gravity in a particular 7D Poincaré-Einstein background that is asymptotically hyperbolic and has the above 6D Einstein manifold at its conformal infinity or boundary. We show the full equivalence of both computations, as an outgrowth of the IR/UV connection in AdS/CFT correspondence, and in this way the timehonoured one-loop calculations in Einstein and higher-derivative gravities take an interesting new turn. ‡

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supporting

confidence: 54%

Section: Resultsmentioning

confidence: 99%

Section: Miscellany: Boundary Factorization Vs Bulk Wkb Exactnessmentioning

confidence: 99%

Section: Non-conformally Flat Case: Poincaré-einstein Metricmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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One-loop divergences in 7D Einstein and 6D conformal gravities

Aros

Bugini

Díaz

2020

J. High Energ. Phys.

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Matching one‐loop divergences in 7D Einstein and 6D Conformal Gravities

2019

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Within the context of AdS/CFT correspondence, we first compute the one-loop infrared (IR) divergences of 7D Einstein gravity in a certain Poincaré-Einstein background metric. Then, we compute the one-loop ultraviolet (UV) divergences of 6D conformal gravity on the conformal boundary. We verify the equality of the above results that stem from the IR-UV connection of the duality dictionary. Key ingredients are heat kernel techniques, factorization of the boundary higher-derivative kinetic operator for the Weyl graviton on the 6D Einstein metric, and Wentzel-Kramers-Brillouin (WKB) exactness of the Einstein graviton in the chosen 7D Poincaré-Einstein background. Overall, we elucidate the way in which the 6D results containing the type-A and type-B conformal anomalies for the Weyl graviton are encoded in the 7D "hologram" given by the fluctuation determinant for the Einstein graviton. We finally discuss possible extensions to include higher-spin fields.

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Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all

Bugini

Díaz

2019

J. High Energ. Phys.

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The holographic Weyl anomaly for GJMS operators (or conformal powers of the Laplacian) are obtained in four and six dimensions. In the context of AdS/CFT correspondence, free conformal scalars with higher-derivative kinetic operators are induced by an ordinary second-derivative massive bulk scalar. At one-loop quantum level, the duality dictionary for partition functions entails an equality between the functional determinants of the corresponding kinetic operators and, in particular, it provides a holographic route to their Weyl anomalies. The heat kernel of a single bulk massive scalar field encodes the Weyl anomaly (type-A and type-B) coefficients for the whole tower of GJMS operators whenever they exist, as in the case of Einstein manifolds where they factorize into product of Laplacians. While a holographic derivation of the type-A Weyl anomaly was already worked out some years back, in this note we compute holographically (for the first time to the best of our knowledge) the type-B Weyl anomaly for the whole family of GJMS operators in four and six dimensions. There are two key ingredients that enable this novel holographic derivation that would be quite a daunting task otherwise: (i) a simple prescription for obtaining the holographic Weyl anomaly for higher-curvature gravities, previously found by the authors, that allows to read off directly the anomaly coefficients from the bulk action; and (ii) an implied WKB-exactness, after resummation, of the heat kernel for the massive scalar on a Poincaré-Einstein bulk metric with an Einstein metric on its conformal infinity. The holographically computed Weyl anomaly coefficients are explicitly verified on the boundary by exploiting the factorization of GJMS operators on Einstein manifolds and working out the relevant heat kernel coefficient. §

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On the Weyl anomaly of 4D conformal higher spins: a holographic approach

Cited by 9 publications

References 92 publications

One-loop divergences in 7D Einstein and 6D conformal gravities

One-loop divergences in 7D Einstein and 6D conformal gravities

Matching one‐loop divergences in 7D Einstein and 6D Conformal Gravities

Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all

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