A soliton menagerie in AdS

TL;DR

This work examines charged scalar solitons in asymptotically global AdS$_4$ across three bulk theories (a phenomenological Abelian–Higgs model and two consistent truncations, $SU(3)$ and $U(1)^4$) to understand when solitons can grow beyond the AdS scale and how they connect to planar, zero-temperature solutions. It reveals a rich, multi-branch soliton structure: some branches emerge perturbatively from AdS, others exist disconnected from AdS, and many branches exhibit critical behavior and bubble-like mergers as the scalar charge $q$ and boundary conditions are varied; notably, in several models the unbounded soliton branches smoothly funnel into planar hairy black holes. The study also leverages double-trace deformations as a tunable dial to probe criticality and inter-branch connectivity, and confirms that in the M2-brane truncation a supersymmetric (BPS) sector yields unbounded charges while non-supersymmetric branches persist and interact with planar limits. Overall, the results establish that global AdS solitons can exhibit complex phase structure and smoothly connect to planar configurations in a controlled limit, with concrete realizations in supergravity truncations and M-theory contexts, providing insight into finite-volume holographic systems and the microcanonical phase diagram of the dual CFTs.

Abstract

We explore the behaviour of charged scalar solitons in asymptotically global AdS4 spacetimes. This is motivated in part by attempting to identify under what circumstances such objects can become large relative to the AdS length scale. We demonstrate that such solitons generically do get large and in fact in the planar limit smoothly connect up with the zero temperature limit of planar scalar hair black holes. In particular, for given Lagrangian parameters we encounter multiple branches of solitons: some which are perturbatively connected to the AdS vacuum and surprisingly, some which are not. We explore the phase space of solutions by tuning the charge of the scalar field and changing scalar boundary conditions at AdS asymptopia, finding intriguing critical behaviour as a function of these parameters. We demonstrate these features not only for phenomenologically motivated gravitational Abelian-Higgs models, but also for models that can be consistently embedded into eleven dimensional supergravity.

Figures (21)

• Figure 1: The scalar potentials for the three models we consider. The $SU(3)$ truncation has the potential with a global minimum at $\phi_{PW}$ and a zero at $\phi_0$. The Ableian-Higgs potential and the $U(1)^4$ truncation have potentials that are unbounded from below, with the latter being exponential (thus steeper) while the former is quadratic.
• Figure 2: $\phi(r)$ for a representative low mass global soliton with $\Delta =2$ boundary condition. For this solution we have chosen $q^2=1.2$ and fixed the point along the branch by fixing $\phi_c=0.05$. At this point we find asymptotic data: $q\mu = 2.001(4), \rho = 0.002(1), m=0.001(9), q\phi_2 = 0.053(6)$ and other near core data: $qA_c = 1.998(4), \beta_c = 0.002(5)$.
• Figure 3:
• Figure 4: (a) The scaling invariants \ref{['dim2invariants']} for the branch connected to global AdS$_4$ in theories where $q>q_c$. Here as a representative example we have chosen $q^2=1.3$. Red is the $m$ invariant, green is the $\phi_2$ invariant and blue is the $\rho$ invariant. The dashed lines indicate these quantities for planar hairy black hole solutions at low temperature. (b) $\phi$ profiles for various points along the branch showing agreement with $\phi$ profiles for planar hairy black holes at low temperature.
• Figure 5: $m(\phi_c)$, for a range of fixed $q$ illustrating the existence of a planar limit even when there is a branch with a mass bounded from above. Each maximum of the bottom branch connects with the corresponding minimum of the top branch as $q$ is increased.