Supersymmetric solitons and a degeneracy of solutions in AdS/CFT

TL;DR

This paper explores supersymmetric solutions in gauged supergravity with AdS asymptotics, revealing a degeneracy of solutions related to Wilson lines and phase transitions, with implications for dual CFT states.

Contribution

It identifies new smooth BPS solutions with Wilson lines in AdS gauged supergravity and demonstrates their degeneracy and phase transition behavior.

Findings

Existence of smooth 1/2 BPS solutions with Wilson lines

Degeneracy of solutions at a special Wilson line value

Phase transition between different supersymmetric saddle-points

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.