Renormalization-Group Improved Effective Potential for Interacting Theories with Several Mass Scales in Curved Spacetime

The renormalization group (RG) is used in order to obtain the RG improved effective potential in curved spacetime. This potential is explicitly calculated for the Yukawa model and for scalar electrodynamics, i.e. theories with several (namely, more than one) mass scales, in a space of constant curvature. Using the $\lambda \varphi^4$-theory on a general curved spacetime as an example, we show how it is possible to find the RG improved effective Lagrangian in curved spacetime. As specific applications, we discuss the possibility of curvature induced phase transitions in the Yukawa model and the effective equations (back-reaction problem) for the $\lambda \varphi^4$-theory on a De Sitter background.Comment: 18 pages, LaTeX file, UB-ECM-PF 93/2

Improved Effective Potential in Curved Spacetime and Quantum Matter - Higher Derivative Gravity Theory

\noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-$R^2$-gravity--- in curved spacetime. The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easiliy obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase trnasitions), are discussed. For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. Stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the Standard Model with the same addition, is numerically analyzed. We show that, in these models, QG tends to make the scalar sector less unstable.Comment: 23 pages, Oct 17 199

Linkage analysis of a kindred with inherited 46,XY partial gonadal dysgenesis

We have reported a kindred in which 46,XY gonadal dysgenesis was inherited in an X-linked (or autosomal dominant sex-limited) manner and in which affected subjects did not have a large duplication of the short arm of the X-chromosome. In the present study we used linkage and sequence analyses to test the role of X-linked and various autosomal genes in the etiology of the familial 46,XY partial gonadal dysgenesis. For analysis of X-linkage, 28 microsatellite polymorphisms and 1 restriction fragment length polymorphism were studied. The genotypes of informative family members were determined at each locus, and data were analyzed. Despite the large number of loci tested, our studies did not establish linkage between the trait and an X-chromosomal locus. With respect to the study of autosomal genes, linkage analysis using a polymorphism within the 3'-untranslated region of the WT1 gene excluded involvement of WT-1 in the etiology of the abnormal gonadal differentiation of the family in this study. Similarly, linkage analysis using four microsatellites on the distal short arm of chromosome 9 was not consistent with linkage. Linkage analysis of a locus close to the SOX9 gene as well as analysis of the coding region of the SOX9 gene suggested that this gene was not associated with the trait in the affected subjects we studied. Our data suggest the role of an autosomal gene in the abnormal gonadal differentiation in the family in the study, but do not formally exclude the role of an X-chromosome gene