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

F. Bugini, D. E. Diaz

Resultado de la investigación: Article

1 Cita (Scopus)

Resumen

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.

Idioma originalEnglish
Número de artículo188
PublicaciónJournal of High Energy Physics
Volumen2019
N.º2
DOI
EstadoPublished - 1 feb 2019

Huella dactilar

anomalies
operators
scalars
coefficients
heat
derivation
dictionaries
kinetics
towers
factorization
ingredients
determinants
infinity
partitions
routes
curvature
gravitation
products

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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abstract = "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 Poincar{\'e}-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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Holographic Weyl anomaly for GJMS operators : one Laplacian to rule them all. / Bugini, F.; Diaz, D. E.

En: Journal of High Energy Physics, Vol. 2019, N.º 2, 188, 01.02.2019.

Resultado de la investigación: Article

TY - JOUR

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AU - Bugini, F.

AU - Diaz, D. E.

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N2 - 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.

AB - 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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