Conformal anomalies in 6D four-derivative theories: A heat-kernel analysis

Casarin, Lorenzo

doi:10.1103/physrevd.108.025014

Cited by 5 publications

(2 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While the utility of heat kernel methods is well-known and they keep being employed in many contexts, see for example [52,53] for some recent applications to trace anomalies, first-quantized methods for treating the graviton with the N = 4 spinning particle are more JHEP10(2023)152 recent and we have championed them here to show their usefulness. In this respect, it would be interesting to extend the present analysis to the first quantized model that describes the N = 0 supergravity [54], i.e.…”

Section: Discussionmentioning

confidence: 99%

Six-dimensional one-loop divergences in quantum gravity from the $$ \mathcal{N} $$ = 4 spinning particle

Bastianelli,

Comberiati,

Fecit

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

In this work, we investigate the computation of the counterterms necessary for the renormalization of the one-loop effective action of quantum gravity using both the worldline formalism and the heat kernel method. Our primary contribution is the determination of the Seleey-DeWitt coefficient a3(D) for perturbative quantum gravity with a cosmological constant, which we evaluate on Einstein manifolds of arbitrary D dimensions. This coefficient characterizes quantum gravity in a gauge-invariant manner due to the on-shell condition of the background on which the graviton propagates. Previously, this coefficient was not fully known in the literature. We employ the $$ \mathcal{N} $$ N = 4 spinning particle model recently proposed to describe the graviton in first quantization and then use the heat kernel method to cross-check the correctness of our calculations. Finally, we restrict to six dimensions, where the coefficient corresponds to the logarithmic divergences of the effective action, and compare our results with those available in the literature.

show abstract

Section: Discussionmentioning

confidence: 99%

Six-dimensional one-loop divergences in quantum gravity from the $$ \mathcal{N} $$ = 4 spinning particle

Bastianelli,

Comberiati,

Fecit

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Heat kernel methods are standard nowadays and they continue to be used in many contexts, as in the recent discussions on trace anomalies [29][30][31]. However, a reformulation in terms of path integrals has its advantages.…”

Section: Introductionmentioning

confidence: 99%

Worldline path integrals for the graviton

Bastianelli,

Damia Paciarini

2024

Class. Quantum Grav.

View full text Add to dashboard Cite

We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant coeﬃcients related to the UV divergences of quantum gravity. These gauge invariant coeﬃcients were previously obtained in arbitrary dimensions through two alternative techniques: the quantization of the N = 4 spinning particle that propagates the graviton on Einstein spaces and the more conventional heat kernel approach. Our worldline path integrals are closer to the latter method and are employed to compute the trace of the heat kernel.

show abstract

Substructures of the Weyl group and their physical applications

Martini,

Paci,

Sauro

et al. 2024

J. High Energ. Phys.

View full text Add to dashboard Cite

We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are chosen such that their composition is associative. Mathematically, apart from rare exceptions, they are partial associative groupoids, not groups, so they do not have an algebra of infinitesimal transformations, but this limitation can be partially circumvented using some of their properties cleverly. We classify and discuss the substructures with two-derivatives differential constraints, the most famous of which being known as the harmonic or restricted Weyl group in the physics literature, but we also show the existence of a lightcone constraint which realizes a proper subgroup of the Weyl group. We then show the physical implications that come from invariance under the two most important substructures, concentrating on classical properties of the energy-momentum tensor and a generalization of the quantum trace anomaly. We also elaborate further on the harmonic substructure, which can be interpreted as partial gauge fixing of full Weyl invariance using BRST methods. Finally, we discuss how to construct differential constraints of arbitrary higher-derivative order and present, as examples, generalizations involving scalar constraints with four and six derivatives.

show abstract

Conformal anomalies in 6D four-derivative theories: A heat-kernel analysis

Cited by 5 publications

References 33 publications

Six-dimensional one-loop divergences in quantum gravity from the $$ \mathcal{N} $$ = 4 spinning particle

Six-dimensional one-loop divergences in quantum gravity from the $$ \mathcal{N} $$ = 4 spinning particle

Worldline path integrals for the graviton

Substructures of the Weyl group and their physical applications

Contact Info

Product

Resources

About