One-loop holographic Weyl anomaly in six dimensions

Liu, James T.; McPeak, Brian

doi:10.1007/jhep01(2018)149

Cited by 8 publications

(15 citation statements)

References 35 publications

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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: 52%

“…In six dimensions, the UV logarithmic divergence is given by the "accumulated" b 6 heat coefficient. The scalar and vector inputs have been known for quite a while, whereas the coefficient for the rank 2 symmetric traceless unconstrained tensor has only recently been reported [13]. We write down the latter in the full A-basis of curvature invariants 1 for future reference We can now apply our shortcut route by restricting to an Einstein metric without spoiling the independence of the four Weyl-invariant terms in the 6D Weyl anomaly basis 2 .…”

Section: D Conformal Gravity: Uv Divergencementioning

confidence: 99%

“…Before closing, it may be of interest to establish a connection with the holographic expectations based on the functional Schrödinger approach [51,52] (see also [13]), namely, that the holographic Weyl anomaly from the one-loop bulk effective action be (41)…”

Section: Miscellany: Boundary Factorization Vs Bulk Wkb Exactnessmentioning

confidence: 99%

“…Our present contribution is twofold. First, we obtain, in one go, all anomaly coefficients by extending the boundary computation to a generic Einstein background, exploiting the factorization into shifted Lichnerowicz operators [12] and making use of the corresponding explicit form of b 6 heat coefficient for the symmetric transverse-traceless two-tensor field [13]. Second, we extend the bulk computation to an asymptotically AdS Poincaré-Einstein metric, with the above Einstein manifolds on its conformal boundary, in order to compute the log-IR divergence of the 7D Einstein graviton.…”

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: 52%

Section: D Conformal Gravity: Uv Divergencementioning

confidence: 99%

Section: Miscellany: Boundary Factorization Vs Bulk Wkb Exactnessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Aros

Bugini

Díaz

2020

J. High Energ. Phys.

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“…Modulo totally derivative terms (including E 6 ), the new hattedÎ i 's involve Riemann polynomials of order i. (In literature, combinations of I i 's based on supersymmetry were discussed in [23][24][25].) In terms of these new combinations, the conformal anomalies are…”

Section: Conformal Anomalies In D =mentioning

confidence: 99%

Holographic (a,c) charges and their universal relation in d=6 from massless higher-order gravities

Lü

Wen

2019

Phys. Rev. D

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Recent studies of holographic properties of massless higher-order gravities, whose linear spectrum contains only the (massless) graviton, yielded some universal relations in d = 4 dimensions between the holographic a, c charges and the overall coefficient factor C T of the energy-momentum tensor two-point function, namely c = 1 d−1 ℓ ∂a ∂ℓ = C T , where ℓ is the AdS radius. The second equality was shown to be valid in all dimensions. In this paper, we establish the first equality in d = 6 by examining these quantities from D = 7 higher-order gravities. Consequently the overall coefficient of the two-point function of the energy-momentum tensor is proportional to this c charge, generalizing the well-known d = 4 result. We identify the relevant c charge as the coefficient of a specific combination of the three type-B anomalies. Modulo total derivatives, this combination involves Riemann tensor at most linearly. †

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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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One-loop holographic Weyl anomaly in six dimensions

Cited by 8 publications

References 35 publications

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

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

Holographic (a,c) charges and their universal relation in d=6 from massless higher-order gravities

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

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