For topological insulator surfaces with two or three Dirac cones, attractive interactions create conformal manifolds of quantum critical fixed points (a ring and two 2-spheres) in the one-loop renormalization group flow.
We follow closely the path outlined in Ref.[64]
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Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points
For topological insulator surfaces with two or three Dirac cones, attractive interactions create conformal manifolds of quantum critical fixed points (a ring and two 2-spheres) in the one-loop renormalization group flow.