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\(\mathcal{N}\)-extended D = 4 supergravity, unconventional SUSY and graphene. (English) Zbl 1434.83153
Summary: We derive a 2+1 dimensional model with unconventional supersymmetry at the boundary of an \(\mathrm{AdS}_4\) \(\mathcal{N}\)-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene-like 2D materials at the two Dirac points, \(\mathbf{K}\) and \(\mathbf{K} '\). The two valleys correspond to the two independent sectors of the \(\mathrm{OSp}(p \vert 2) \times \mathrm{OSp} (q \vert 2)\) boundary model in the \(p = q\) case, which are related by a parity transformation. The Semenoff and Haldane-type masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model.

83E50 Supergravity
81T60 Supersymmetric field theories in quantum mechanics
58J28 Eta-invariants, Chern-Simons invariants
83E05 Geometrodynamics and the holographic principle
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