TY - JOUR

T1 - Perturbative c-theorem in d-dimensions

AU - Yonekura, Kazuya

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Field Theories in Lower Dimensions

KW - Renormalization Group

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U2 - 10.1007/JHEP04(2013)011

DO - 10.1007/JHEP04(2013)011

M3 - Article

AN - SCOPUS:84876354138

SN - 1029-8479

VL - 2013

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 4

M1 - 11

ER -