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

Bastianelli, Fiorenzo; Comberiati, Francesco; Fecit, Filippo; Ori, Fabio

doi:10.1007/jhep10(2023)152

Cited by 4 publications

(1 citation statement)

References 65 publications

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“…We have verified the correctness of the one-loop gauge invariant coefficients for quantum gravity with cosmological constant obtained in [15]. The calculation of an additional gauge invariant coefficient, namely the one that in six dimensions corresponds to the on-shell logarithmic divergences, has been computed very recently [48]. In general, these coefficients characterize in a gauge invariant way how standard pure quantum gravity diverges in the ultraviolet, giving some information on how additional degrees of freedom carried by possible UV completions should act.…”

Section: Discussionmentioning

confidence: 53%

Worldline path integrals for the graviton

Bastianelli,

Damia Paciarini

2024

Class. Quantum Grav.

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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.

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Section: Discussionmentioning

confidence: 53%

Worldline path integrals for the graviton

Bastianelli,

Damia Paciarini

2024

Class. Quantum Grav.

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Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions

Basile,

Joung,

2024

J. High Energ. Phys.

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We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian constraints which generate the coadjoint orbits of another, dual, Lie group. In case of (inhomogeneous) orthogonal groups, the dual groups are (centrally-extended inhomogeneous) symplectic groups. This defines a symplectic dual pair correspondence between the coadjoint orbits of the isometry group and those of the dual Lie group, whose quantum version is the reductive dual pair correspondence à la Howe. We show explicitly how various particle species arise from the classification of coadjoint orbits of Poincaré and (A)dS symmetry. In the Poincaré case, we recover the data of the Wigner classification, which includes continuous spin particles, (spinning) tachyons and null particles with vanishing momenta, besides the usual massive and massless spinning particles. In (A)dS case, our classification results are not only consistent with the pattern of the corresponding unitary irreducible representations observed in the literature, but also contain novel information. In dS, we find the presence of partially massless spinning particles, but continuous spin particles, spinning tachyons and null particles are absent. The AdS case shows the largest diversity of particle species. It has all particles species of Poincaré symmetry except for the null particle, but allows in addition various exotic entities such as one parameter extension of continuous particles and conformal particles living on the boundary of AdS. Notably, we also find a large class of particles living in “bitemporal” AdS space, including ones where mass and spin play an interchanged role. We also discuss the relative inclusion structure of the corresponding orbits.

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Worldline path integral for the massive graviton

Fecit

2024

Eur. Phys. J. C

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We compute the counterterms necessary for the renormalization of the one-loop effective action of massive gravity from a worldline perspective. This is achieved by employing the recently proposed massive $$\mathcal {N}=4$$ N = 4 spinning particle model to describe the propagation of the massive graviton on those backgrounds that solve the Einstein equations without cosmological constant, namely on Ricci-flat manifolds, in four dimensions. The model is extended to be consistent in D spacetime dimensions by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, together with the inclusion of a suitable Chern–Simons term. Then, constructing the worldline path integral on the one-dimensional torus allows for the correct calculation of the one-loop divergencies in arbitrary D dimensions. Our primary contribution is the determination of the Seleey–DeWitt coefficients up to the fourth coefficient $$a_3(D)$$ a 3 ( D ) , which to our knowledge has never been reported in the literature. Its calculation is generally laborious on the quantum field theory side, as a general formula for these coefficients is not available for operators that are non-minimal in the heat kernel sense. This work illustrates the computational efficiency of worldline methods in this regard. Heat kernel coefficients characterize linearized massive gravity in a gauge-independent manner due to the on-shell condition of the background on which the graviton propagates. They could serve as a benchmark for verifying alternative approaches to massive gravity, and, for this reason, their precise expression should be known explicitly.

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

Cited by 4 publications

References 65 publications

Worldline path integrals for the graviton

Worldline path integrals for the graviton

Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions

Worldline path integral for the massive graviton

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