Curved spacetime effective field theory (cEFT) — construction with the heat kernel method

Nakonieczny, Łukasz

doi:10.1007/jhep01(2019)034

Cited by 12 publications

(7 citation statements)

References 58 publications

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“…and R µν is the Ricci tensor and R µνρσ is the Riemann tensor. Yet, as was pointed out in [8], in the case when the Ricci scalar is non-zero the dominant contributions will come from terms linear in R. Moreover, in what follows we will not discuss the curvature contribution to dimension six operators, that is we will set c GdHdH = 0 and consider c dHdH and c 6 independent of the Ricci scalar. This is justified by the fact that curvature dependent parts of these coefficients are suppressed by additional powers of m 2 X as compared to the terms proportional only to λ HX .…”

Section: Jhep11(2020)132mentioning

confidence: 99%

“…The next step is to obtain cEFT for the scalar H that will be valid at energy and curvature scales smaller than m X . To this end, we will follow [8] and integrate out the heavy Z 2 -symmetric real scalar singlet X. Having done this we may write the action functional for our cEFT as…”

Section: Jhep11(2020)132mentioning

confidence: 99%

“…Recently, there has been a renewed influx of efforts at writing down the systematic way of producing EFT from a set of minimal assumptions about new particles sector [4][5][6][7]. In an effort to extend this approach to curved spacetime the formalism of the curved spacetime EFT has been recently developed in [8].…”

Section: Introductionmentioning

confidence: 99%

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Two interacting scalars system in curved spacetime — vacuum stability from the curved spacetime Effective Field Theory (cEFT) perspective

Lalak

Nakonieczna

Nakonieczny

2020

J. High Energ. Phys.

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In this article we investigated the influence of the gravity mediated higher dimensional operators on the issue of vacuum stability in a model containing two interacting scalar fields. As a framework we used the curved spacetime Effective Field Theory (cEFT) applied to the aforementioned system in which one of the scalars is heavy. After integrating out the heavy scalar we used the standard Euclidean approach to the obtained cEFT. Apart from analyzing the influence of standard operators like the non-minimal coupling to gravity and the dimension six contribution to the scalar field potential, we also investigated the rarely discussed dimension six contribution to the kinetic term and the new gravity mediated contribution to the scalar quartic self-interaction.

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Section: Jhep11(2020)132mentioning

confidence: 99%

Section: Jhep11(2020)132mentioning

confidence: 99%

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Two interacting scalars system in curved spacetime — vacuum stability from the curved spacetime Effective Field Theory (cEFT) perspective

Lalak

Nakonieczna

Nakonieczny

2020

J. High Energ. Phys.

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“…Heat kernel expansions are very important, such as the Schwinger-DeWitt expansion in the induced gravity on the AdS background [22]. The heat kernel method applies to calculate effective actions [23], such as the effective field theory in curved spacetime [24,25], the heat kernel expansion and the one-loop effective action in QCD [26], the Seeley-DeWitt expansion for the one-loop effective action in the Einstein-Maxwell theory [27], the one-loop effective action for the modified Gauss-Bonnet gravity [28] and in dS 2 and AdS 2 spacetime [29], ϕ 4 -fields [30], and various operators [31][32][33]. The heat kernel method also applies to calculate vacuum energies, such as Casimir energies in curved spacetime [34][35][36][37] and in spherically symmetric backgrounds [38].…”

Section: Introductionmentioning

confidence: 99%

Scattering approach for calculating one-loop effective action and vacuum energy

Li¹,

Chen²,

Li³

et al. 2022

Preprint

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An approach for calculating one-loop effective actions and vacuum energies is suggested. Spectral functions are functions of the eigenvalue spectrum of an operator. The starting point is to regard one-loop effective actions and vacuum energies in quantum field theory and scattering phase shifts and amplitudes in quantum mechanics as spectral functions of an operator. Different spectral functions of the same operator may belong to different fields of physics. Methods for calculating various spectral functions can be interconverted through transform relations among spectral functions. In this paper, we convert the method for calculating scattering phase shifts and amplitudes to a method for calculating one-loop effective actions and vacuum energies. In principle, all methods for the calculation of scattering phase shifts and amplitudes can be converted to methods for the calculation of the one-loop effective actions and vacuum energies. As an example, we convert the Born approximation in quantum-mechanical scattering theory to a method for calculating one-loop effective actions and vacuum energies. In appendices, we provide integral representations of the Bessel function for calculating the sum encountered.

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“…Yukawa interactions have also been considered in related calculations: the asymptotic safety program for quantum gravity [24][25][26][27][28], in perturbative quantum gravity [29], in unimodular gravity [30][31][32], and in scaleinvariant gravity [33]. Some other recent work that is relevant includes [34] where nonperturbative effects in the effective action with Abelian gauge fields and Yukawa terms is considered; [35,36] who who examine the role of Yukawa couplings in curved spacetime, but with no gauge fields.…”

Section: Introductionmentioning

confidence: 99%

Yang-Mills Yukawa model in curved spacetime

Toms

2019

Preprint

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The one-loop effective action for the scalar field part of a non-Abelian gauge theory based on a general gauge group of the form G × U (1), where the gauge group G is arbitrary, is calculated. A complex scalar field, both Abelian and non-Abelian gauge fields and Dirac fermions coupled to gauge and scalar fields are included. A general mass term for the Dirac fields that includes a pseudoscalar term as well as both scalar and pseudoscalar Yukawa couplings is considered. The background field method is used in its manifestly gauge condition independent and gauge invariant form to isolate the divergent part of the one-loop effective action and to calculate the associated renormalisation group functions. Terms in the renormalised effective action up to and including those quadratic in the curvature are calculated using renormalisation group methods. The background scalar field is not assumed to be constant, so the second order derivative terms in the effective action can be calculated, and the gravitational background is kept arbitrary. The difference between the gauge condition independent approach and the more standard approach where gauge condition dependent results are found is demonstrated by explicit calculations. The anomaly that can arise if the pseudoscalar mass term for the fermions is transformed away from the classical theory is noted.

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Curved spacetime effective field theory (cEFT) — construction with the heat kernel method

Cited by 12 publications

References 58 publications

Two interacting scalars system in curved spacetime — vacuum stability from the curved spacetime Effective Field Theory (cEFT) perspective

Two interacting scalars system in curved spacetime — vacuum stability from the curved spacetime Effective Field Theory (cEFT) perspective

Scattering approach for calculating one-loop effective action and vacuum energy

Yang-Mills Yukawa model in curved spacetime

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