Strong-weak coupling duality in anisotropic current interactions

TL;DR

This paper explores the all-orders beta function in anisotropic current interactions, revealing dualities and phase structures including sine-Gordon, sinh-Gordon, Kosterlitz-Thouless, and cyclic RG trajectories.

Contribution

It introduces a novel analysis of the beta function using strong-weak coupling duality and topology, extending RG flows and identifying new phase behaviors.

Findings

Identification of sine-Gordon, sinh-Gordon, and Kosterlitz-Thouless phases

Discovery of an additional phase with cyclic or roaming RG trajectories

Extension of RG flows to arbitrarily large or small scales

Abstract

The recently proposed all orders beta function is further investigated. By using a strong-weak coupling duality of the beta function, and some added topology of the space of couplings we are able to extend the flows to arbitrarily large or small scales. Using a non-trivial RG invariant we are able to identify sine-Gordon, sinh-Gordon and Kosterlitz-Thouless phases. We also find an additional phase with cyclic or roaming RG trajectories.