C-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow

Year: 2015

Authors: Bacṣ V., Defenu N., Trombettoni A., Nàndori I.

Autors Affiliation: Univ Debrecen, H-4010 Debrecen, Hungary; SISSA, I-34136 Trieste, Italy; CNR IOM DEMOCRITOS Simulat Ctr, I-34136 Trieste, Italy; MTA DE Particle Phys Res Grp, H-4001 Debrecen, Hungary; MTA Atomki, H-4001 Debrecen, Hungary.

Abstract: In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency beta(2), where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (beta(2) < 8 pi) to the infra-red limit is in good quantitative agreement with the expected Delta c = 1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation) is crucial to get sensible results even when a single frequency is used. Journal/Review: NUCLEAR PHYSICS B

Volume: 901      Pages from: 444  to: 460

More Information: The authors gratefully thank A. Codello, G. Delfino, B. Lima De Souza, G. Mussardo, I.G. Marian, R. Percacci and G. Takacs for useful discussions during the preparation of this work. This work was supported by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences. Support from the CNR/MTA Italy-Hungary 2013-2015 Joint Project Non-perturbative field theory and strongly correlated systems is gratefully acknowledged. A.T. acknowledge support from the CNR project ABNANOTECH.
DOI: 10.1016/j.nuclphysb.2015.11.001

Citations: 12
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