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Register a new user$mathcal{N}$-Extended $D=4$ Supergravity, Unconventional SUSY and Graphene
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We derive a $2+1$ dimensional model with unconventional supersymmetry at the boundary of an ${rm AdS}_4$ $mathcal{N}$-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, ${bf K}$ and ${bf K}$. The two valleys correspond to the two independent sectors of the ${rm OSp}(p|2)times {rm OSp}(q|2)$ 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.
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We formulate a unimodular N=1, d=4 supergravity theory off shell. We see that the infinitesimal Grassmann parameters defining the unimodular supergravity transformations are constrained and show that the conmutator of two infinitesinal unimodular supergravity transformations closes on transverse diffeomorphisms, Lorentz transformations and unimodular supergravity transformations. Along the way, we also show that the linearized theory is a supersymmetric theory of gravitons and gravitinos. We see that de Sitter and anti-de Sitter spacetimes are non-supersymmetric vacua of our unimodular supergravity theory.
Extreme near-horizon geometries in D=11 supergravity preserving four supersymmetries are classified. It is shown that the Killing spinors fall into three possible orbits, corresponding to pairs of spinors defined on the spatial cross-sections of the horizon which have isotropy groups SU(3), G2, or SU(4). In each case, the conditions on the geometry and the 4-form flux are determined. The integrability conditions obtained from the Killing spinor equations are also investigated.
We put forward a unimodular $N=1, d=4$ anti-de Sitter supergravity theory off shell. This theory, where the Cosmological Constant does not couple to gravity, has a unique maximally supersymmetric classical vacuum which is Anti-de Sitter spacetime with radius given by the equation of motion of the auxiliary scalar field, ie, $S=frac{3}{kappa L}$. However, we see that the non-supersymmetric classical vacua of the unimodular theory are Minkowski and de Sitter spacetimes as well as anti-de Sitter spacetime with radius $l eq L$.
We report on recent results in the study of extremal black hole attractors in N=2, d=4 ungauged Maxwell-Einstein supergravities. For homogeneous symmetric scalar manifolds, the three general classes of attractor solutions with non-vanishing Bekenstein-Hawking entropy are discussed. They correspond to three (inequivalent) classes of orbits of the charge vector, which sits in the relevant symplectic representation R_{V} of the U-duality group. Other than the 1/2-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The complete classification of the U-duality orbits, as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon), is also reviewed. Finally, we consider the analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attractors yield a related moduli space.
The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two approaches is explicitly given for various quantities; superconformal gauge fields, curvatures and curvature constraints, general conformal multiplets and their transformation laws, and so on. In particular, we carefully analyze the curvature constraints leading to the superconformal algebra and also the superconformal gauge fixing leading to Poincare supergravity since they look rather different between two approaches.
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