The quantum theory of a quadratic gravity theory derived from the heterotic string effective action

The renormalizability of a quadratic gravity theory with exponential coupling between dilaton field and curvature terms is verified. The wave function for this model is then deduced to first order in e −Φ g2 4 by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the potential is slowly varying with respect to Φ. It is shown how formal expressions for the average paths in minisuperspace {〈a(t)〉, 〈Φ(t)〉} for this theory can be used to determine the shifts from the classical solutions acl(t) and Φcl(t), which occur only at third order in the expansion of the functional integrals representing the expectation values. * Present address: Institut für Mathematik, Universität Potsdam, D-14415 Potsdam, Germany Given a dimensionless metric and scalar field, the most general renormalizable sigma model coupled to gravity [1] is I = ∫ dx √−g [ b1(φ)( φ) 2 + b2(φ)(∇μφ)(∇φ) φ+ b3(φ)[(∇μφ)(∇φ)] + b4(φ)(∇μφ)(∇φ) + b5(φ) + c1(φ)R(∇νφ)(∇φ) + c2(φ)R (∇μφ)(∇νφ) + c3(φ)R φ+ a1(φ)RμναβR + a2(φ)RμνR μν + a3(φ)R 2 + a4(φ)R ]