90007338

open access

Version of Record

Wilson action for the O(N) model

English (英語)

Nuclear Physics B

956

115022-115022

Elsevier B.V.

2020-07

2020-08-04

In this paper the fixed-point Wilson action for the critical O(N) model in D=4−ϵ dimensions is written down in the ϵ expansion to order ϵ2. It is obtained by solving the fixed-point Polchinski Exact Renormalization Group equation (with anomalous dimension) in powers of ϵ. This is an example of a theory that has scale and conformal invariance despite having a finite UV cutoff. The energy-momentum tensor for this theory is also constructed (at zero momentum) to order ϵ2. This is done by solving the Ward-Takahashi identity for the fixed point action. It is verified that the trace of the energy-momentum tensor is proportional to the violation of scale invariance as given by the exact RG, i.e., the β function. The vanishing of the trace at the fixed point ensures conformal invariance. Some examples of calculations of correlation functions are also given.

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This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3