Extension of Hölder’s theorem in

Akhmedov, Azer

doi:10.1017/etds.2014.132

Cited by 20 publications

(45 citation statements)

References 5 publications

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“…and the comparison with Eq. (40) shows that this quadratic term is also negligible with the tree-level one in the regime (67). This improvement over what the result (77) would suggest comes from the fact that the quadratic term in φ in the tree-level Lagrangian includes a contribution from the n = 1 term in the expansion (53), which is much greater than the contribution from the n = 2 term whenK ′′χ ≪K ′ .…”

Section: Further Analysis For the Casek ′′χ ≪K ′mentioning

confidence: 93%

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Quantum field theory of K-mouflage

Brax

Valageas

2016

Phys. Rev. D

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We consider K-mouflage models, which are K-essence theories coupled to matter. We analyze their quantum properties and in particular the quantum corrections to the classical Lagrangian. We setup the renormalization program for these models and show that, contrary to renormalizable field theories where renormalization by infinite counterterms can be performed in one step, K-mouflage theories involve a recursive construction whereby each set of counterterms introduces new divergent quantum contributions which in turn must be subtracted by new counterterms. This tower of counterterms can be in principle constructed step by step by recursion and allows one to calculate the finite renormalized action of the model. In particular, it can be checked that the classical action is not renormalized and that the finite corrections to the renormalized action contain only higher-derivative operators. We concentrate then on the regime where calculability is ensured, i.e., when the corrections to the classical action are negligible. We establish an operational criterion for classicality and show that this is satisfied in cosmological and astrophysical situations for (healthy) K-mouflage models which pass the Solar System tests. These results rely on perturbation theory around a background and are only valid when the background configuration is quantum stable. We analyze the quantum stability of astrophysical and cosmological backgrounds and find that models that pass the Solar System tests are quantum stable. We then consider the possible embedding of the K-mouflage models in an Ultra-Violet completion. We find that the healthy models which pass the Solar System tests all violate the positivity constraint which would follow from the unitarity of the putative UV completion, implying that these healthy K-mouflage theories have no UV completion. We then analyze their behavior at high energy, and we find that the classicality criterion is satisfied in the vicinity of a high-energy collision, implying that the classical K-mouflage theory can be applied in this context. Moreover, the classical description becomes more accurate as the energy increases, in a way compatible with the classicalization concept.

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Section: Further Analysis For the Casek ′′χ ≪K ′mentioning

confidence: 93%

“…All these quantities diverge at large k and must be regularized. As is well known [39,40], introducing a high-energy cutoff, k < Λ c , leads to incorrect results because it breaks the symmetries of the system (Lorentz invariance). Therefore, we use dimensional regularization [42,43].…”

Section: Appendix A: One-loop Contribution To the Vacuum Energy Densitymentioning

confidence: 99%

Quantum field theory of K-mouflage

Brax

Valageas

2016

Phys. Rev. D

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“…Actually, as discovered in [36], elaborated in e.g. [37], and extensively reviewed in [38], there is more to the story.…”

Section: A Primer On Quantum Correctionsmentioning

confidence: 99%

The quantum swampland

Danielsson

2019

J. High Energ. Phys.

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“…We can now calculate the potential vacuum energy corresponding to the potential (24). Obviously, the contribution of the Yukawa terms will coincide with that calculated in the preceding section and will be given by the formula (16). Then we have the "eight"-diagram type contribution of the quartic scalarpseudoscalar interaction…”

Section: Wess-zumino Model Without Auxiliary Fields and The Vacuum Enmentioning

confidence: 78%

“…Recently, this Pauli-Zeldovich cancellation mechanism for the divergences of the vacuum energy due to the balance between the contributions of bosons and fermions has attracted growing attention [10,11,12,13,14]. Similar questions were also discussed in papers [15,16,17,18,19]. In particular, in [14] several models with interactions between different particles at the lowest order of the perturbation theory were considered.…”

Section: Introductionmentioning

confidence: 95%

Comment about the vanishing of the vacuum energy in the Wess–Zumino model

2018

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We check the cancellation of the vacuum energy in the Wess-Zumino model at the two-loop order in the component field formalisms with and without auxiliary fields. We show that in both cases the vacuum energy is equal to zero. However, in the formalism where the auxiliary fields are excluded, the vanishing of the vacuum energy arises due to the cancellation between the potential and kinetic energies, while in the formalism with the auxiliary fields, both terms vanish separately.

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Extension of Hölder’s theorem in

Cited by 20 publications

References 5 publications

Quantum field theory of K-mouflage

Quantum field theory of K-mouflage

The quantum swampland

Comment about the vanishing of the vacuum energy in the Wess–Zumino model

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