Article

# Induced Einstein-Hilbert-Yang-Mills action from quantum effects in generalized Kaluza-Klein theory

Blackett Laboratory, Imperial College, London SW7 2BZ, UK

Physics Letters B (Impact Factor: 6.13). 02/1984; 135(4):283-287. DOI: 10.1016/0370-2693(84)90392-7 **ABSTRACT**

It is shown how the Einstein-Hilbert-Yang-Mills action may be induced from quantized matter fields on a non-abelian Kaluza-Klein background. General formulae are derived in the case of a quantized scalar field when the extra dimensions form a coset space. Explicit results are obtained in the special case of odd-dimensional spheres.

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**ABSTRACT:**We study the problem of quantized matter fields on a non-abelian Kaluza-Klein background. It is shown how the Einstein-Hilbert-Yang-Mills action may be induced from quantum effects. A new method of calculating the low curvature limit of the effective action is presented and used to derive general formulae for the terms in the induced action arising from scalar and spinor fields in the case where the extra dimensions form a coset space. Explicit results for the induced cosmological, gravitational, and gauge-coupling constant are found when the extra dimensions are odd-dimensional spheres. Current address: Department of Theoretical Physics, University of Newcastle Upon Tyne, Newcastle Upon Tyne NE1 7RU, England.Nuclear Physics B 01/1984; 245:161-188. DOI:10.1016/0550-3213(84)90428-0 · 3.93 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The effective action for spinor fields propagating in a time-dependent Kaluza-Klein background geometry is calculated explicitly to one-loop order in an adiabatic approximation. This result is used in a stability analysis of the Candelas-Weinberg model. It is found that the “internal” space (which we choose to be an odd-dimensional sphere SN) is stable against small, uniform oscillations only if the ratio of the number of scalar fields to the number of spinor fields is greater than a certain minimum value.It is also shown that oscillations of the internal space produce conformal gravity waves in the four-dimensional space.Nuclear Physics B 09/1984; 244(1-244):173-185. DOI:10.1016/0550-3213(84)90188-3 · 3.93 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The higher-dimensional spacetime: (flat spacetime)*times; SU(2) is investigated, from the viewpoint of induced gravity, whether it is suitable as a vacuum in Kaluza-Klein theory. It is shown that such a vacuum is really a self-consistent solution of induced gravity and becomes stable against the change of scale of internal space by adjusting parameters such as the mass of matter fields, cosmological constant and so on.Progress of Theoretical Physics 01/1985; 73(1):306-309. DOI:10.1143/PTP.73.306 · 1.45 Impact Factor

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