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RG flows of non-diagonal minimal models perturbed by $\phi_{1,3}$
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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.
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Cited by 1 Pith paper
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Selection rules for RG flows of minimal models
A constructive enumeration of all local minimal-model CFTs, organized by Jones index, yields selection rules for RG flows that recover known results and predict new ones.
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