TY - JOUR

T1 - Renormalization group patterns and c-theorem in more than two dimensions

AU - Cappelli, Andrea

AU - JoséIgnacio Latorre, Latorre

AU - Vilasís-Cardona, Xavier

N1 - Funding Information:
We want to thank J.L. Cardy, PH. Damgaard, G. Shore and A.B. Zamolod-chikov for useful discussions. This work has been supported by CYCIT and the EEC Science Twinning grant SC1000337. X. V. acknowledges the support of an FF1 grant.

PY - 1992/6/15

Y1 - 1992/6/15

N2 - We elaborate on a previous attempt to prove the irreversibility of the renormalization group flow in more than two dimensions. This involves the construction of a monotonically decreasing c-function using a spectral representation. The missing step of the proof is a good definition of this function at the fixed points. We argue that for all kinds of perturbative flows the c-function is well defined and the c-theorem holds in any dimension. We provide examples in multicritical and multicomponent scalar theories for dimension 2 < d < 4. We also discuss the non-perturbative flows in the yet unsettled case of the O(N) sigma model for 2 ≤ d ≤ 4 and large N.

AB - We elaborate on a previous attempt to prove the irreversibility of the renormalization group flow in more than two dimensions. This involves the construction of a monotonically decreasing c-function using a spectral representation. The missing step of the proof is a good definition of this function at the fixed points. We argue that for all kinds of perturbative flows the c-function is well defined and the c-theorem holds in any dimension. We provide examples in multicritical and multicomponent scalar theories for dimension 2 < d < 4. We also discuss the non-perturbative flows in the yet unsettled case of the O(N) sigma model for 2 ≤ d ≤ 4 and large N.

UR - http://www.scopus.com/inward/record.url?scp=0001671444&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(92)90119-V

DO - 10.1016/0550-3213(92)90119-V

M3 - Article

AN - SCOPUS:0001671444

SN - 0550-3213

VL - 376

SP - 510

EP - 538

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -