We derive a 2+1 dimensional model with unconventional supersymmetry at the boundary of an 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, K and K′. The two valleys correspond to the two independent sectors of the OSp(p|2) × OSp(q|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.

中文翻译：

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N$$ \mathcal{N} $$ -extended D = 4 超重力，非常规 SUSY 和石墨烯

我们在 AdS$_{4} \mathcal{N} $ -extended supergravity 的边界推导出了一个具有非常规超对称性的 2+1 维模型，概括了之前的结果。边界模型的（非常规）扩展超对称性有助于在自上而下的方法中描述两个狄拉克点 K 和 K' 处的类石墨烯 2D 材料的电子特性。这两个谷对应于 p = q 情况下 OSp(p|2) × OSp(q|2) 边界模型的两个独立扇区，它们通过奇偶变换相关。进入相应狄拉克方程的 Semenoff 和 Haldane 型质量与模型中基材的扭转参数一致。