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Register a new user3D gauged supergravity from SU(2) reduction of $N=1$ 6D supergravity
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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 $mathbf{R}^3times mathbf{R}^{textrm{dim}, G}$.
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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 find a large class of supersymmetric domain wall solutions from six-dimensional $N=(2,2)$ gauged supergravity with various gauge groups. In general, the embedding tensor lives in $mathbf{144}_c$ representation of the global symmetry $SO(5,5)$. We explicitly construct the embedding tensors in $mathbf{15}^{-1}$ and $overline{mathbf{40}}^{-1}$ representations of $GL(5)sim mathbb{R}^+times SL(5)subset SO(5,5)$ leading to $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)ltimesmathbb{R}^4_{boldsymbol{s}}$ gauge groups, respectively. These gaugings can be obtained from $S^1$ reductions of seven-dimensional gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)$ gauge groups. As in seven dimensions, we find half-supersymmetric domain walls for purely magnetic or purely electric gaugings with the embedding tensors in $mathbf{15}^{-1}$ or $overline{mathbf{40}}^{-1}$ representations, respectively. In addition, for dyonic gauge groups with the embedding tensors in both $mathbf{15}^{-1}$ and $overline{mathbf{40}}^{-1}$ representations, the domain walls turn out to be $frac{1}{4}$-supersymmetric as in the seven-dimensional analogue. By the DW/QFT duality, these solutions are dual to maximal and half-maximal super Yang-Mills theories in five dimensions. All of the solutions can be uplifted to seven dimensions and further embedded in type IIB or M-theories by the well-known consistent truncation of the seven-dimensional $N=4$ gauged supergravity.
We continue the study of supersymmetric domain wall solutions in six-dimensional maximal gauged supergravity. We first give a classification of viable gauge groups with the embedding tensor in $mathbf{5}^{+7}$, $bar{mathbf{5}}^{+3}$, $mathbf{10}^{-1}$, $mathbf{24}^{-5}$, and $overline{mathbf{45}}^{+3}$ representations of the off-shell symmetry $GL(5)subset SO(5,5)$. We determine an explicit form of the embedding tensor for gauge groups arising from each representation together with some examples of possible combinations among them. All of the resulting gauge groups are of a non-semisimple type with abelian factors and translational groups of different dimensions. We find $frac{1}{2}$- and $frac{1}{4}$-supersymmetric domain walls with $SO(2)$ symmetry in $SO(2)ltimes mathbb{R}^8$ and $SO(2)ltimes mathbb{R}^6$ gauge groups from the embedding tensor in $mathbf{24}^{-5}$ representation and in $CSO(2,0,2)ltimes mathbb{R}^4$, $CSO(2,0,2)ltimes mathbb{R}^2$, and $CSO(2,0,1)ltimes mathbb{R}^4$ gauge groups with the embedding tensor in $overline{mathbf{45}}^{+3}$ representations. These gauge groups are parametrized by a traceless matrix and electrically and magnetically embedded in $SO(5,5)$ global symmetry, respectively.
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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