Conformal anomalies for interacting scalar fields in curved spacetime
Abstract
The occurrence of anomalies in the trace of the energymomentum tensor for scalar field theories in curved spacetime is discussed. For the special case of spherical spacetime, an O(n+1)covariant formalism is used to rederive the standard freefield anomaly in four dimensions, and to calculate the anomaly in six dimensions. It is then shown that for an interacting scalar field theory there is a further contribution to the trace anomaly proportional to the renormalization group β function. This assertion is then checked by explicit calculations in φ^{4} theory in four dimensions and φ^{3} theory in six dimensions and values for the anomaly found to fourth order in the renormalized coupling constants λ and g. Finally, these results are generalized to the case of an arbitrary background spacetime, where it is shown that the introduction of a positiondependent coupling constant λ(x) enables the relation between the trace anomaly and the β function to be expressed in the form T^{μ}_{Iμ}=β(λ)δW_{I}δλ(x)_{λ(x)=λ}. where W_{I} is the sum over vacuum bubble diagrams with interactions.
 Publication:

Physical Review D
 Pub Date:
 February 1979
 DOI:
 10.1103/PhysRevD.19.1134
 Bibcode:
 1979PhRvD..19.1134D