# Confinement of charged tachyons in AdS spacetime

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...

• Could you please give a link to the paper? – Frederic Brünner Jul 7 '14 at 12:04
• @FredericBrünner I added the link. Specifically, the quote and the choice of $m^2$ are on page 6. – ScroogeMcDuck Jul 7 '14 at 16:04