Perturbative \(c\)-theorem in \(d\)-dimensions. (English) Zbl 1342.81330
Summary: We study perturbative behavior of free energies on a d-dimensional sphere Sd for theories with marginal interactions. The free energies are interpreted as the “dilaton effective action” with the dilaton having a nontrivial background vacuum expectation value. We compute the dependence of the free energies on the radius of the sphere by using dimensional regularization. It is shown that the first (second) derivative of the free energies in odd (even) dimensions with respect to the radius of the sphere are proportional to the square of the beta functions of coupling constants. The result is consistent with the c, F and a-theorems in two, three, four and six dimensions. The result is also used to rule out a large class of scale invariant theories which are not conformally invariant.
MSC:
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
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