R-Twisting and 4d/2d Correspondences

Understand

We show how aspects of the R-charge of N=2 CFTs in four dimensions are encoded in the q-deformed Kontsevich-Soibelman monodromy operator, built from their dyon spectra.

• In particular, the monodromy operator should have finite order if the R-charges are rational.
• We verify this for a number of examples including those arising from pairs of ADE singularities on a Calabi-Yau threefold (some of which are dual to 6d (2,0) ADE theories suitably fibered over the plane).
• In these cases we find that our monodromy maps to that of the Y-systems, studied by Zamolodchikov in the context of TBA.