RG flows of non-diagonal minimal models perturbed by $\phi_{1,3}$

TL;DR

This paper analyzes the renormalization group flows of non-diagonal minimal models perturbed by the $_{1,3}$ operator, revealing structure and classification of flows within the Cappelli, Itzykson, Zuber scheme.

Contribution

It provides a perturbative analysis of $_{1,3}$ flows in minimal models, proposing a comprehensive classification and conjecture of all possible flows for large m.

Findings

(A,A) models flow to (A,A), (A,D) to (A,D)

No cross-series hopping occurs between (A,A) and (A,D)

Identifies three isolated flows of type (E,A) to (A,E)

Abstract

Studying perturbatively, for large m, the torus partition function of both (A,A) and (A,D) series of minimal models in the Cappelli, Itzykson, Zuber classification, deformed by the least relevant operator $\phi_{(1,3)}$, we disentangle the structure of $\phi_{1,3}$ flows. The results are conjectured on reasonable ground to be valid for all m. They show that (A,A) models always flow to (A,A) and (A,D) ones to (A,D). No hopping between the two series is possible. Also, we give arguments that there exist 3 isolated flows (E,A)-->(A,E) that, together with the two series, should exhaust all the possible $\phi_{1,3}$ flows. Conservation (and symmetry breaking) of non-local currents along the flows is discussed and put in relation to the A,D,E classification.