Do the gravitational corrections to the beta functions of the quartic and Yukawa couplings have an intrinsic physical meaning?
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2017
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Elsevier Science BV
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Abstract
We study the beta functions of the quartic and Yukawa couplings of General Relativity and Unimodular Gravity coupled to the λφ4 and Yukawa theories with masses. We show that the General Relativity corrections to those beta functions as obtained from the 1PI functional by using the standard MS multiplicative renormalization scheme of Dimensional Regularization are gauge dependent and, further, that they can be removed by a non-multiplicative, though local, field redefinition. An analogous analysis is carried out when General Relativity is replaced with Unimodular Gravity. Thus we show that any claim made about the change in the asymptotic behavior of the quartic and Yukawa couplings made by General Relativity and Unimodular Gravity lack intrinsic physical meaning.
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© 2017 The Authors. Published by Elsevier B.V. We are grateful to E. Álvarez for illuminating discussions. This work has received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grants agreement No 674896 and No 690575. We also have been partially supported by the Spanish MINECO through grants FPA2014-54154-P and FPA2016-78645-P, COST actions MP1405 (Quantum Structure of Spacetime) and COST MP1210 (The string theory Universe). S.G-M acknowledges the support of the Spanish Research Agency (Agencia Estatal de Investigación) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597.