Unique effective action in five-dimensional Kaluza-Klein theory

We study the question of the gauge dependence of the quantum gravity contribution to the running gauge coupling constant for electromagnetism. The calculations are performed using dimensional regularization in a manifestly gauge invariant and gauge condition independent formulation of the effective action. It is shown that there is no quantum gravity contribution to the running charge, and hence there is no alteration to asymptotic freedom at high energies as predicted by 11.10.Gh, 11.10.Hi Until fairly recently the belief that quantum gravity lay outside the realm of any conceivable experimental test was pervasive in the physics community. Important work by Donoghue [1] helped to change this pessimistic viewpoint. Donoghue proposed that the effective field theory methodology be applied to quantum gravity, with Einstein's theory viewed as an effective low energy approximation to some as yet unknown more complete theory. Since Donoghue's pioneering work, there has been considerable interest in this viewpoint. A beautiful review of the subject has been given by Burgess [2].A notable calculation was performed recently by Robinson and Wilczek [3] for Einstein gravity coupled to a gauge theory. It was claimed, as a consequence of quantum gravity corrections, that all gauge theories become asymptotically free at high energies. This includes the Einstein-Maxwell theory, and occurs below the Planck scale at which perturbative quantum gravity calculations become suspect. If the gravitational scale is sufficiently low, as predicted by many higher dimensional theories, then it is conceivable that the predictions of [3] on the running gauge coupling constant might be experimentally testable [4]. A recent analysis of the calculation [5] has cast doubt on the results of [3] by claiming that the quantum gravity correction to the running gauge coupling constant is gauge dependent, and that there is really no such effect. The calculations of [5] do demonstrate that when computed using traditional background-field methods the effective action does depend on the choice of gauge condition. Choosing a particular gauge condition, and demonstrating independence of parameters that enter this condition is not sufficient to demonstrate gauge condition independence. As we will discuss, with the choice of gauge conditions made in [3, 5] a gauge condition independent result for the effective action necessitates additional terms that are not present if the standard background-field method is employed. Because of the interest in this problem, its potential as an experimental test of quantum gravity, and the controversy surround- * URL: http://www.staff.ncl.ac.uk/d.j.toms ; Electronic address: d.j.toms@newcastle.ac.uk ing the details, we will present a different analysis to that of [3,5] that removes all question of any possible gauge dependence.There are two basic problems that need to be dealt with in any calculation in a gauge theory. The first is to ensure that the calculations are done in a way that is gauge invariant. The second is ...

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“…[14]. Earlier applications to quantum gravity were given by [15,16], and a more complete reference to other applications can be found in [11,17].…”

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confidence: 99%

“…If any other gauge choice is made, this is no longer the case and additional terms in the connection beyond the Christoffel terms arise to ensure independence of the effective action on the gauge condition. (An illustration of this for quantum gravity is given in [14]. )…”

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confidence: 99%

Quantum gravity and charge renormalization

Toms

2007

Phys. Rev. D

107

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“…It is also shown in this work that the one loop effective potential is gauge dependent, and in fact could be gauged away within a class of gauges by appropriate choice of a gauge parameter . The issue of gauge dependence of the effective action has been extensively analyzed in the past [see [3] and the references therein]. It has also been pointed out that the effective action is not only gauge dependent but also depends upon field reparameterization [4].…”

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confidence: 99%

Gauge-free Coleman–Weinberg potential

Bhattacharjee

Majumdar

2013

Eur. Phys. J. C

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The gauge-dependence of the one loop Coleman-Weinberg effective potential in scalar electrodynamics is resolved using a gauge-free approach not requiring any gauge-fixing of quantum fluctuations of the photon degrees of freedom. This leads to a unique dynamical ratio at one loop of the Higgs mass to the photon mass. We compare our approach and results with those obtained in geometric framework of DeWitt and Vilkovisky, which maintains invariance under field redefinitions as well as invariance under background gauge transformations, but requires, in contrast to our approach, gauge fixing of fluctuating photon fields. We also discuss possible modifications of the Coleman-Weinberg potential if we adapt the DeWitt-Vilkovisky method to our gauge-free approach for scalar QED.

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“…The choice of distance does not show up in the effective action when the background field satisfies the classical equations of motion (on shell), but does when loop corrections modify these equations as in self-consistency. After the effective action theory was modified by introducing a unique distance (a field metric), independent of the choice of fields, i.e., after the Vilkovisky-DeWitt [6,7] (VD) theory was introduced, the KK program expanded back to the original KK dimension (five) [8,9]. However, because the one-loop graviton operator in VD theory cannot be made minimal except for simple background spaces, e.g., Af 4 x5' 1 x • • xS\ progress has been extremely slow [10,11].…”

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confidence: 99%

Unique one-loop effective action for the six-dimensional Einstein-Hilbert action

Cho

Kantowski

1991

Phys. Rev. Lett.

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In this Letter we give the gauge-independent divergent part of the one-loop correction to the effective action for the six-dimensional Einstein-Hilbert action, including a cosmological constant. We extend the methods of Barvinsky-Vilkovisky from four to higher dimensions, including the Vilkovisky-DeWitt correction, to obtain the unique counterterms for an arbitrary background field. All one-loop operators are given for TV dimensions; however, due to the complexity of the Schwinger-DeWitt expansion, going beyond six dimensions to eight or ten will probably require restricting the background.

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Unique effective action in five-dimensional Kaluza-Klein theory

Cited by 62 publications

References 13 publications

Quantum gravity and charge renormalization

Quantum gravity and charge renormalization

Gauge-free Coleman–Weinberg potential

Unique one-loop effective action for the six-dimensional Einstein-Hilbert action

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