The /d=6 trace anomaly from quantum field theory fourloop graphs in one dimension
Abstract
We calculate the integrated trace anomaly for a real spin0 scalar field in six dimensions in a torsionless curved space without a boundary. We use a pathintegral approach for a corresponding supersymmetric quantum mechanical model. Weyl ordering the corresponding Hamiltonian in phase space, an extra twoloop counterterm {1}/{8}(R+g ^{ij}Γ ^{l}_{ki}Γ ^{k}_{lj}) is produced in the action. Applying a recursive method we evaluate the components of the metric tensor in Riemann normal coordinates in six dimensions and construct the interaction lagrangian density by employing the background field method. The calculation of the anomaly is based on the endpoint scalar propagator and not on the string inspired centerofmass propagator which gives incorrect results for the local trace anomaly. The manipulation of the Feynman diagrams is partly relied on the factorization of fourdimensional subdiagrams and partly on a brute force computer algebra program developed to serve this specific purpose. The computer program enables one to perform index contractions of twelve quantum fields (10 395 in the present case) a task which cannot be accomplished otherwise. We observe that the contribution of the disconnected diagrams is no longer proportional to the twodimensional trace anomaly (which vanishes in four dimensions). The integrated trace anomaly is finally expressed in terms of the 17 linearly independent scalar monomials constructed out of covariant derivatives and Riemann tensors.
 Publication:

Nuclear Physics B
 Pub Date:
 October 2001
 DOI:
 10.1016/S05503213(01)000980
 arXiv:
 arXiv:hepth/0103073
 Bibcode:
 2001NuPhB.613..237H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 23 pages, 17 figures