On the Trace Anomaly as a Measure of Degrees of Freedom

Details On the Trace Anomaly as a Measure of Degrees of Freedom On the Trace Anomaly as a Measure of Degrees of Freedom

2000-05-12

arxiv.org/abs/hep-th/0005115v1

Phys.Lett. B487 (2000) 87-95

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 14 pages, 2 tables

Scientific paper

10.1016/S0370-2693(00)00809-1

Recent conjectures of the c-theorem in four and higher dimensions have suggested that the coefficient of the Euler characteristic in the trace anomaly could measure the degrees of freedom in field theory and decrease along the renormalization-group flow. We compute this quantity for free massless scalar, fermion and antisymmetric tensor fields in any dimension, and analyse its dependence on spin and space-time dimension. In the limit of large number of dimensions, where the theories become semiclassical, we find that this quantity does not approach the classical number of field components, but is enhanced for spinful particles. This seemingly strange behaviour is found to be consistent with known renormalization-group patterns and a specific c-theorem conjecture.

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