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Register a new userNew Vacua of Gauged N=8 Supergravity
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We analyze a particular SU(2) invariant sector of the scalar manifold of gauged N=8 supergravity in five dimensions, and find all the critical points of the potential within this sector. The critical points give rise to Anti-de Sitter vacua, and preserve at least an SU(2) gauge symmetry. Consistent truncation implies that these solutions correspond to Anti-de Sitter compactifications of IIB supergravity, and hence to possible near-horizon geometries of 3-branes. Thus we find new conformal phases of softly broken N=4 Yang--Mills theory. One of the critical points preserves N=2 supersymmetry in the bulk and is therefore completely stable, and corresponds to an N=1 superconformal fixed point of the Yang--Mills theory. The corresponding renormalization group flow from the N=4 point has c_{IR}/c_{UV} = 27/32. We also discuss the ten-dimensional geometries corresponding to these critical points.
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Type IIB string theory on a 5-sphere gives rise to ${cal N}=8, SO(6)$ gauged supergravity in five dimensions. Motivated by the fact that this is the context of the most widely studied example of the AdS/CFT correspondence, we undertake an investigation of its critical points. The scalar manifold is an $E_{6(6)}/USp(8)$ coset, and the challenge is that it is 42-dimensional. We take a Machine Learning approach to the problem using TensorFlow, and this results in a substantial increase in the number of known critical points. Our list of 32 critical points contains all five of the previously known ones, including an ${cal N}=2$ supersymmetric point identified by Khavaev, Pilch and Warner.
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 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 $mathbf{R}^3times mathbf{R}^{textrm{dim}, G}$.
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.
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