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 -