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Register a new userA note on the Hyper--CR equation, and gauged $N=2$ supergravity
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We construct a new class of solutions to the dispersionless hyper--CR equation, and show how any solution to this equation gives rise to a supersymmetric Einstein--Maxwell cosmological space--time in $(3+1)$--dimensions.
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We discuss a possibility of restricting parameters in $mathcal{N}=2$ supergravity based on axion observations. We derive conditions that prepotential and gauge couplings should satisfy. Such conditions not only allow us to constrain the theory but also provide the lower bound of $mathcal{N}=2rightarrowmathcal{N}=1$ breaking scale.
We construct black holes with scalar hair in a wide class of four-dimensional N=2 Fayet-Iliopoulos gauged supergravity theories that are characterized by a prepotential containing one free parameter. Considering the truncated model in which only a single real scalar survives, the theory is reduced to an Einstein-scalar system with a potential, which admits at most two AdS critical points and is expressed in terms of a real superpotential. Our solution is static, admits maximally symmetric horizons, asymptotically tends to AdS space corresponding to an extremum of the superpotential, but is disconnected from the Schwarzschild-AdS family. The condition under which the spacetime admits an event horizon is addressed for each horizon topology. It turns out that for hyperbolic horizons the black holes can be extremal. In this case, the near-horizon geometry is AdS_2 x H^2, where the scalar goes to the other, non-supersymmetric, critical point of the potential. Our solution displays fall-off behaviours different from the standard one, due to the fact that the mass parameter $m^2=-2/ell^2$ at the supersymmetric vacuum lies in a characteristic range $m^2_{BF}le m^2le m^2_{rm BF}+ell^{-2}$ for which the slowly decaying scalar field is also normalizable. Nevertheless, we identify a well-defined mass for our spacetime, following the prescription of Hertog and Maeda. Quite remarkably, the product of all horizon areas is not given in terms of the asymptotic cosmological constant alone, as one would expect in absence of electromagnetic charges and angular momentum. Our solution shows qualitatively the same thermodynamic behaviour as the Schwarzschild-AdS black hole, but the entropy is always smaller for a given mass and AdS curvature radius. We also find that our spherical black holes are unstable against radial perturbations.
We consider $mathfrak{gl}_2$-invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also derive the actions of the twisted monodromy matrix entries onto twisted off-shell Bethe vectors.
We obtain Yang-Mills $SU(2)times G$ gauged supergravity in three dimensions from $SU(2)$ group manifold reduction of (1,0) six dimensional supergravity coupled to an anti-symmetric tensor multiplet and gauge vector multiplets in the adjoint of $G$. The reduced theory is consistently truncated to $N=4$ 3D supergravity coupled to $4(1+textrm{dim}, G)$ bosonic and $4(1+textrm{dim}, G)$ fermionic propagating degrees of freedom. This is in contrast to the reduction in which there are also massive vector fields. The scalar manifold is $mathbf{R}times frac{SO(3,, textrm{dim}, G)}{SO(3)times SO(textrm{dim}, G)}$, and there is a $SU(2)times G$ gauge group. We then construct $N=4$ Chern-Simons $(SO(3)ltimes mathbf{R}^3)times (Gltimes mathbf{R}^{textrm{dim}G})$ three dimensional gauged supergravity with scalar manifold $frac{SO(4,,1+textrm{dim}G)}{SO(4)times SO(1+textrm{dim}G)}$ and explicitly show that this theory is on-shell equivalent to the Yang-Mills $SO(3)times G$ gauged supergravity theory obtained from the $SU(2)$ reduction, after integrating out the scalars and gauge fields corresponding to the translational symmetries $mathbf{R}^3times mathbf{R}^{textrm{dim}, G}$.
In this paper, we study the Dirac equation for an electron constrained to move on a catenoid surface. We decoupled the two components of the spinor and obtained two Klein-Gordon-like equations. Analytical solutions were obtained using supersymmetric quantum mechanics for two cases, namely, the constant Fermi velocity and the position-dependent Fermi velocity cases.
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