Asymptotic safety in the sine-Gordon model

TL;DR

This paper demonstrates that the 2D sine-Gordon model has a nontrivial UV fixed point, making it asymptotically safe, with implications for its high-energy behavior and duality with the massive sine-Gordon model.

Contribution

It identifies a nontrivial UV fixed point in the sine-Gordon model using the functional renormalization group, establishing asymptotic safety in this context.

Findings

Presence of a nontrivial UV fixed point

Singularity indicating the model's energy-scale limit

Duality with the massive sine-Gordon model

Abstract

In the framework of the functional renormalization group method it is shown that the phase structure of the 2-dimensional sine-Gordon model possesses a nontrivial UV fixed point which makes the model asymptotically safe. The fixed point exhibits strong singularity similarly to the scaling found in the vicinity of the infrared fixed point. The singularity signals the upper energy-scale limit to the validity of the model. We argue that the sine-Gordon model with a momentum-dependent wavefunction renormalization is in a dual connection with the massive sine-Gordon model.