It is well known that the negative cosmological constant of AdS spacetime can act like a confining potential. That is, in contrast to asymptotically flat spacetime, in an asymptotically AdS spacetime *massive particles cannot escape to infinity*. However, massless particles can escape to infinity and actually do so in a finite time.

**As tachyons travel faster than massless particles, is it true that all tachyons can escape to infinity as well?**

If the answer is yes, then I have some trouble understanding the following argument in a paper by Horowitz on holographic superconductivity (see here). Here, the considered action of the holographic dual to the superconductor (the bulk action) is

$S=\int d^4x\sqrt{-g}\left(R+\frac{6}{L^2}-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-|\nabla\Psi-iqA\Psi|^2-m^2|\Psi|^2\right)$,

i.e., a complex scalar field $\Psi$ and a Maxwell field $A_t$ (electric) coupled to gravity. The effective mass for $\Psi$ following from this action is
$m_{eff}^2=m^2+q^2g^{tt}A_t^2$.

In constructing this dual theory, Horowitz argues that "*In AdS, the charged particles cannot escape, since the negative
cosmological constant acts like a confining box, and they settle outside the horizon.*" (Of course, only for particles for which the sign of the charge is the same as that of the black hole.)

However, the case considered subsequently is $m^2=-\frac{2}{L^2}$, which implies that $m_{eff}^2<0$ since also $g^{tt}<0$. Hence they consider tachyons!

**Being tachyons, how can these particles settle outside the horizon? Why would they be confined by the cosmological constant rather than escape to infinity?**

EDIT: right now I'm actually questioning my claim that all tachyons automatically travel faster than light...

This post imported from StackExchange Physics at 2014-07-08 08:15 (UCT), posted by SE-user ScroogeMcDuck