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

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 infrared 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 also including 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.

9 pages, 4 figures, v1, to be published on Nucl. Phys. B

References in corpus (3)

• Asymptotic safety: a simple example
• Lectures on renormalization and asymptotic safety
• Comparison of renormalization group schemes for sine-Gordon type models

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• Topological phase transitions in four dimensions
• Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(\varphi )R$ coupling
• Exact Renormalization Group and Sine Gordon Theory
• Lattice sine-Gordon model
• Holographic Beta functions for the Generalized Sine Gordon Theory