Abstract
We derive a 2+1 dimensional model with unconventional supersymmetry at the boundary of an AdS4 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.
Highlights
1 2 ωij where ωij, A and ψA are one-forms, while J, T and Q are the generators of Lorentz, internal gauge and supersymmetry transformations, respectively
We consider a three dimensional model of unconventional supersymmetry at the boundary of an AdS4 supergravity vacuum, extending the analysis in [12], where it was shown that the three-dimensional AVZ model could be holographically realized as the boundary theory of an N = 2 four-dimensional supergravity of the AdS4 spacetime
We briefly elaborate on a microscopic description of graphene-like materials which can account for the massive Dirac equations that we find at the two Dirac points
Summary
We are interested into the AdS4 boundary, which is reached in the limit r → ∞. Consistency of the boundary conditions requires that both V 3 and dV 3 vanish at the boundary This is the case since, at the boundary, ω3i ∧ Ei = 0 (by virtue of the general properties of the extrinsic curvature of the boundary) and (Ψ∓)Ψ± ∝ ηAB (ψA)T σ2ψB = 0, the latter being a consequence of the antisymetry of σ2 and the symmetry of ηAB. These fields can be consistently set to zero: Aa1b2 = 0 This condition, is not optional, implicit in the requirement that the fields at the boundary (and in particular the gravitini fields) satisfy consistent equations.
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