Generalising the staircase models

TL;DR

This paper introduces generalized integral equations extending staircase models, providing analytical and numerical evidence for new roaming renormalisation group trajectories in relativistic field theories, revealing complex flow patterns between conformal and massive theories.

Contribution

It develops a generalized framework of integral equations for staircase models, uncovering new roaming RG trajectories connecting coset conformal field theories and massive theories.

Findings

Existence of new roaming RG trajectories

Trajectories connect coset CFTs to massive theories

Numerical and analytical support for the models

Abstract

Systems of integral equations are proposed which generalise those previously encountered in connection with the so-called staircase models. Under the assumption that these equations describe the finite-size effects of relativistic field theories via the Thermodynamic Bethe Ansatz, analytical and numerical evidence is given for the existence of a variety of new roaming renormalisation group trajectories. For each positive integer $k$ and $s=0,\dots, k-1$, there is a one-parameter family of trajectories, passing close by the coset conformal field theories $G^{(k)}\times G^{(nk+s)}/G^{((n+1)k+s)}$ before finally flowing to a massive theory for $s=0$, or to another coset model for $s \neq 0$.