Conformal anomaly in 4D gravity-matter theories non-minimally coupled witha dilaton

The conformal anomaly for 4D gravity-matter theories, which are non-minimal ly coupled with the dilaton, is systematically studied. Special care is tak en of rescaling of fields, treatment of total derivatives, hermiticity of t he system operator and the choice of measure. Scalar, spinor and vector fie lds are taken as the matter quantum fields and their explicit conformal ano malies in the gravity-dilaton background are found. The cohomology analysis is carried out and some new conformal invariants and trivial terms, involv ing the dilaton, are obtained. The symmetry of the constant shift of the di laton field plays an important role. The general structure of the conformal anomaly is examined. it is shown that the dilaton affects the conformal an omaly characteristically for each case: (1) [Scalar] The dilaton changes th e conformal anomaly only by a new conformal invariant, I-4; (2) [Spinor] Th e dilaton does not change the conformal anomaly; (3) [Vector] The dilaton c hanges the conformal anomaly by three new (generalized) conformal invariant s, I-4, I-2, I-1. We present some new anomaly formulae which are useful for practical calculations. Finally, the anomaly induced action is calculated for the dilatonic Wess-Zumino model. We point out that the coefficient of t he total derivative term in the conformal anomaly for the 2D scalar coupled to a dilaton is ambiguous. This resolves the disagreement between earlier calculations and the result of Hawking and Bousso. (C) 1999 Elsevier Scienc e B.V.