Supersymmetric solitons and a degeneracy of solutions in AdS/CFT

Abstract

We study Lorentzian supersymmetric configurations in $D=4$ and $D=5$ gauged $\mathcal{N}=2$ supergravity. We show that there are smooth $1/2$ BPS solutions which are asymptotically AdS${}_4$ and AdS${}_5$ with a planar boundary, a compact spacelike direction and with a Wilson line on that circle. There are solitons where the $S^1$ shrinks smoothly to zero in the interior, with a magnetic flux through the circle determined by the Wilson line, which are AdS analogues of the Melvin fluxtube. There is also a solution with a constant gauge field, which is pure AdS. Both solutions preserve half of the supersymmetries at a special value of the Wilson line. There is a phase transition between these two saddle-points as a function of the Wilson line precisely at the supersymmetric point. Thus, the supersymmetric solutions are degenerate, at least at the supergravity level. We extend this discussion to one of the Romans solutions in four dimensions when the Euclidean boundary is $S^1\times {\Sigma }_g$ where ${\Sigma }_g$ is a Riemann surface with genus $g>0$. We speculate that the supersymmetric state of the CFT on the boundary is dual to a superposition of the two degenerate geometries.

25 pages, 2 figures

References in corpus (8)

• Building an AdS/CFT superconductor
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Charging axisymmetric space-times with cosmological constant
• Euclidean Black Saddles and AdS${}_4$ Black Holes
• Euclidean Supergravity
• Geometry of AdS-Melvin Spacetimes
• New non-extremal and BPS hairy black holes in gauged $\mathcal{N}=2$ and $\mathcal{N}=8$ supergravity
• Exact holographic RG flows in extended SUGRA

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• Phase transitions for charged planar solitons in AdS
• Complexity, scaling, and a phase transition
• Spin Structures and AdS${}_4$ Holography
• Classical and quantum chaos of closed strings on a charged confining holographic background
• Neutralizing Topological Obstructions to Bubbles of Nothing
• Light dilaton near critical points in top-down holography
• Holographic Krylov complexity in the Coulomb branch of $\mathcal{N}=4$ SYM
• Instability of supersymmetric black holes via quantum phase transitions
• Vacuum configuration of winding superstrings from non-standard semiclassical quantization
• Exact scalar (quasi-)normal modes of black holes and solitons in gauged SUGRA