Renormalization of the Periodic Scalar Field Theory by Polchinski's Renormalization Group Method
The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this paper, we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.
I. Nandori et al., "Renormalization of the Periodic Scalar Field Theory by Polchinski's Renormalization Group Method," Journal of Physics G: Nuclear and Particle Physics, vol. 28, no. 4, pp. 607-616, IOP Publishing, Apr 2002.
The definitive version is available at https://doi.org/10.1088/0954-3899/28/4/302
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