Perturbative c-theorem in d-dimensions

Kazuya Yonekura

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15 Citations (Scopus)


We study perturbative behavior of free energies on a d-dimensional sphere S d 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.

Original languageEnglish
Article number11
JournalJournal of High Energy Physics
Issue number4
Publication statusPublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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