Coupled minimal models revisited

TL;DR

This paper investigates coupled minimal models in the large rank limit, revealing non-trivial IR fixed points with irrational characteristics and demonstrating the breaking of certain symmetries, suggesting the emergence of irrational CFTs.

Contribution

It provides the first detailed analysis of IR fixed points in coupled minimal models at large rank, showing their irrational nature and symmetry breaking patterns.

Findings

Identification of two non-trivial IR fixed points with irrational anomalous dimensions.

Demonstration that for N>4, all currents up to spin 10 are broken in the IR.

Evidence of irrationality in anomalous dimension matrices and insights into quantum Regge trajectories.

Abstract

We study coupled unitary Virasoro minimal models in the large rank ($m \rightarrow \infty$) limit. In large $m$ perturbation theory, we find two non-trivial IR fixed points which exhibit irrational coefficients in several anomalous dimensions and the central charge. For $N>4$ copies, we show that the IR theory breaks all possible currents that would otherwise enhance the Virasoro algebra, up to spin 10. This provides strong evidence that the IR fixed points are examples of compact, unitary, irrational CFTs with the minimal amount of chiral symmetry. We also analyze anomalous dimension matrices for a family of degenerate operators with increasing spin. These display further evidence of irrationality and begin to reveal the form of the leading quantum Regge trajectory.