On stability of nonthermal states in strongly coupled gauge theories

Low-energy thermal equilibrium states of strongly coupled \({\cal N}=4\) supersymmetric Yang-Mills (SYM) theory on a three-sphere are unstable with respect to fluctuations breaking the global \(SO(6)\) R-symmetry. Using the gauge theory/gravity correspondence, a large class of initial conditions in the R-symmetry singlet sector of the theory was been identified that fail to thermalize \cite{Buchel:2013uba,Balasubramanian:2014cja}. A toy model realization of such states is provided by {\it boson stars}, a stationary gravitational configurations supported by a complex scalar field in \(AdS_5\)-gravity. Motivated by the SYM example, we extend the boson star toy model to include the global \(SO(6)\) R-symmetry. We show that sufficient light boson stars in the R-symmetry singlet sector are stable with respect to linearized fluctuations. As the mass of the boson star increases, they do suffer tachyonic instability associated with their localization on \(S^5\). This is opposite to the behaviour of small black holes (dual to equilibrium states of \({\cal N}=4\) SYM) in global \(AdS_5\): the latter develop tachyonic instability as they become sufficiently light. Based on analogy with light boson stars, we expect that the R-symmetry singlet nonthermal states in strongly coupled gauge theories, represented by the quasiperiodic solutions of \cite{Balasubramanian:2014cja}, are stable with respect to linearized fluctuations breaking the R-symmetry.