Corpus ID: 16058232

On conformally covariant powers of the Laplacian

@article{Juhl2011OnCC,
  title={On conformally covariant powers of the Laplacian},
  author={A. Juhl},
  journal={arXiv: Differential Geometry},
  year={2011}
}
  • A. Juhl
  • Published 2011
  • Mathematics, Physics
  • arXiv: Differential Geometry
We propose and discuss recursive formulas for conformally covariant powers $P_{2N}$ of the Laplacian (GJMS-operators). For locally conformally flat metrics, these describe the non-constant part of any GJMS-operator as the sum of a certain linear combination of compositions of lower order GJMS-operators (primary part) and a second-order operator which is defined by the Schouten tensor (secondary part). We complete the description of GJMS-operators by proposing and discussing recursive formulas… Expand
Heat kernel expansions, ambient metrics and conformal invariants
The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-orderExpand
Explicit Formulas for GJMS-Operators and Q-Curvatures
We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincaré–Einstein metrics and renormalized volumeExpand
On partition function and Weyl anomaly of conformal higher spin fields
Abstract We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in theExpand
On higher spin partition functions
We observe that the partition function of the set of all free massless higher spins s = 0, 1, 2, 3,... in flat space is equal to one: the ghost determinants cancel against the 'physical' ones or,Expand
On conformal powers of the Dirac operator on spin manifolds
The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic constructionExpand
Conformally covariant differential operators acting on spinor bundles and related conformal covariants
Conformal powers of the Dirac operator on semi Riemannian spin manifolds are investigated. We give a new proof of the existence of conformal odd powers of the Dirac operator on semi Riemannian spinExpand
Free □k scalar conformal field theory
A bstractWe consider the generalizations of the free U(N ) and O(N ) scalar conformal field theories to actions with higher powers of the Laplacian □k, in general dimension d. We study the spectra,Expand
Entanglement entropy for even spheres
The coefficient of the logarithmic term in the entropy on even spheres is re-computed by the local technique of integrating the finite temperature energy density up to the horizon on staticExpand
Evaluation of spherical GJMS determinants
An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a sum formula for the logdet inExpand
A family of Riesz distributions for differential forms on Euclidian space
In this paper we introduce a new family of operator-valued distributions on Euclidian space acting by convolution on differential forms. It provides a natural generalization of the important RieszExpand
...
1
2
3
...

References

SHOWING 1-10 OF 53 REFERENCES
Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus
Abstract: We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differentialExpand
Laplacian Operators and Q-curvature on Conformally Einstein Manifolds
A new definition of canonical conformal differential operators Pk (k = 1,2,...), with leading term a kth power of the Laplacian, is given for conformally Einstein manifolds of any signature. TheseExpand
Conformally invariant powers of the Laplacian — A complete nonexistence theorem
Conformally invariant operators and the equations they determine play a central role in the study of manifolds with pseudo-Riemannian, Riemannian, conformai and related structures. This observationExpand
Universal recursive formulae for Q-curvatures
Abstract We formulate and discuss two conjectures concerning recursive formulae for Branson's Q-curvatures. The proposed formulae describe all Q-curvatures on manifolds of all even dimensions inExpand
Sharp inequalities, the functional determinant, and the complementary series
Results in the spectral theory of differential operators, and recent results on conformally covariant differential operators and on sharp inequalities, are combined in a study of functionalExpand
Anti-de Sitter space and holography
Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product ofExpand
Conformal geometry, contact geometry, and the calculus of variations
for metricsg in the conformal class of g0, where we use the metric g to view the tensor as an endomorphism of the tangent bundle and where σk d notes the trace of the induced map on the kth exteriorExpand
The Ambient Obstruction Tensor and Q-Curvature
|W |, where W denotes the Weyl tensor. A generalization of the Bach tensor to higher even dimensional manifolds was indicated in [FG1]. This “ambient obstruction tensor”, which, suitably normalized,Expand
Analysis on the minimal representation of O(p;q) { I. Realization via conformal geometry
Abstract This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely the minimal unitary representation of an indefinite orthogonal group; thisExpand
A non-local action for the trace anomaly
Abstract We investigate that portion of the quantum effective action in a curved four-dimensional background determined by the trace anomaly. A covariant, nonlocal action expandable around flat spaceExpand
...
1
2
3
4
5
...