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Unconventional supersymmetry at the boundary of \(\mathrm{AdS}_{4}\) supergravity. (English) Zbl 1390.83359
Summary: In this paper we perform, in the spirit of the holographic correspondence, a particular asymptotic limit of \(\mathcal{N}=2 \), \(\mathrm{AdS}_{4}\) supergravity to \(\mathcal{N}=2 \) supergravity on a locally \(\mathrm{AdS}_{3}\) boundary. Our boundary theory enjoys OSp\((2 | 2) \times \)SO(1,2) invariance and is shown to contain the \(D=3\) super-Chern Simons OSp\((2 | 2)\) theory considered in [P. D. Alvarez et al., J. High Energy Phys. 2012, No. 4, Paper No. 058, 11 p. (2012; Zbl 1348.81394)] and featuring “unconventional local supersymmetry”. The model constructed in that reference describes the dynamics of a spin-1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to be relevant for the description of graphene, near the Dirac points, for specific spatial geometries. Our construction yields the model in [loc. cit.] with a specific prescription on the parameters. In this framework the Dirac spin-1/2 fermion originates from the radial components of the gravitini in \(D=4\).

MSC:
83E50 Supergravity
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60 Supersymmetric field theories in quantum mechanics
58J28 Eta-invariants, Chern-Simons invariants
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