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Register a new userRotating black holes in the FI-gauged $N=2$, $D=4$ $overline{mathbb{C}text{P}}^n$ model
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We construct supersymmetric black holes with rotation or NUT charge for the $overline{mathbb{C}text{P}}^n$- and the $text{t}^3$ model of $N=2$, $D=4$ $text{U}(1)$ FI-gauged supergravity. The solutions preserve 2 real supercharges, which are doubled for their near-horizon geometry. For the $overline{mathbb{C}text{P}}^n$ model we also present a generalization to the nonextremal case, which turns out to be characterized by a Carter-Plebanski-type metric, and has $n+3$ independent parameters, corresponding to mass, angular momentum as well as $n+1$ magnetic charges. We discuss the thermodynamics of these solutions, obtain a Christodoulou-Ruffini mass formula, and shew that they obey a first law of thermodynamics and that the product of horizon areas depends on the angular momentum and the magnetic charges only. At least some of the BPS black holes that we obtain may become instrumental for future microscopic entropy computations involving a supersymmetric index.
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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 generalize the vacuum static black brane solutions of Einsteins equations with negative cosmological constant recently discussed in literature, by introducing rotations and an electromagnetic field. We investigate numerically the thermodynamical properties of the charged and of the rotating $AdS$ black brane and we provide evidences for the existence of the charged and rotating case. In particular, we study the influence of the rotation and charge on the tension and mass. We find that the rotation essentially influences the tensions while the charge essentially influences the mass.
In this paper, we analyze the static solutions for the $U(1)^{4}$ consistent truncation of the maximally supersymmetric gauged supergravity in four dimensions. Using a new parametrization of the known solutions it is shown that for fixed charges there exist three possible black hole configurations according to the pattern of symmetry breaking of the (scalars sector of the) Lagrangian. Namely a black hole without scalar fields, a black hole with a primary hair and a black hole with a secondary hair respectively. This is the first, exact, example of a black hole with a primary scalar hair, where both the black hole and the scalar fields are regular on and outside the horizon. The configurations with secondary and primary hair can be interpreted as a spontaneous symmetry breaking of discrete permutation and reflection symmetries of the action. It is shown that there exist a triple point in the thermodynamic phase space where the three solution coexist. The corresponding phase transitions are discussed and the free energies are written explicitly as function of the thermodynamic coordinates in the uncharged case. In the charged case the free energies of the primary hair and the hairless black hole are also given as functions of the thermodynamic coordinates.
We study fractional Skyrmions in a $mathbb{C}P^2$ baby Skyrme model with a generalization of the easy-plane potential. By numerical methods, we find stable, metastable, and unstable solutions taking the shapes of molecules. Various solutions possess discrete symmetries, and the origin of those symmetries are traced back to congruencies of the fields in homogeneous coordinates on $mathbb{C}P^2$.
The $mathbb{C}P^{N-1}$ sigma model at finite temperature is studied using lattice Monte Carlo simulations on $S_{s}^{1} times S_{tau}^{1}$ with radii $L_{s}$ and $L_{tau}$, respectively, where the ratio of the circumferences is taken to be sufficiently large ($L_{s}/L_{tau} gg 1$) to simulate the model on $mathbb{R} times S^1$. We show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as $L_{tau}$ is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. We find that the global PSU($N$)=SU($N$)$/{mathbb Z}_{N}$ symmetry remains unbroken at quantum and classical levels for the small and large $L_{tau}$, respectively: in the small $L_tau$ region for finite $N$, the order parameter fluctuates extensively with its expectation value consistent with zero after taking an ensemble average, while in the large $L_tau$ region the order parameter remains small with little fluctuations. We also calculate the thermal entropy and find that the degrees of freedom in the small $L_{tau}$ regime are consistent with $N-1$ free complex scalar fields, thereby indicating a good agreement with the prediction from the large-$N$ study for small $L_{tau}$.
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