### Plasma-Ball Duals of Black Holes

#### Posted by urs

Ofer Aharony and Micha Berkooz are visiting Hamburg. Yesterday they gave talks on recent work.

Ofer Aharony spoke about

O. Aharony, S. Minwalla, T. Wiseman
**Plasma-Balls in Large $N$ Gauge Theories and Localized Black Holes**

hep-th/0507219

The central idea here is a qualitative argument which is supposed to say that in the large $N$ limit of $\mathrm{SU}(N)$ gauge theories with a first order confining/deconfining phase transition the free energy – and hence the pressure – of the deconfining phase should pass through 0 close to the phase transition.

The basis for this is the observation that the free energy of the confining phase scales like 0th powers of $N$, while that of the deconfining phase scales with ${N}^{2}$. Hence for both to match at the phase transition point the free energy of the deconfining phase is imagined to be of the form

where $\rho $ is the energy density and $f(\rho )$ is a function that becomes at least very small close to the transition point ${\rho}_{\mathrm{crit}}$. Since $Z$ should probably also be monotonic it is argued to be plausible that it actually goes through 0.

Aharony, Minwalla and Wiseman assume that this is the case. They argue that therefore close to the critical density the pressure vanishes and expect this to result in the existence of stable bubbles of quark-gluon plasma.

Given that idea, it is possibly sort of natural to suspect that these plasma balls might be dual, under AdS/CFT-like dualities, to certain black holes in a dual gravity theory.

A list of qualitative and order-of-magnitude consistency checks of this proposal is then disucssed. For instance it is imagined that Hawking radiation on the gravity side is dual to what is called ‘hadronization’ for the plasma balls. This is the process by which a piece of quark-gluon plasma condeses to a hadron which is then spit out of the plasma ball.

By this process both the black hole and the plasma ball are thought to eventually shrink (even though they are ‘classically stable’, which on the plasma ball side corresponds to the vanishing of its internal pressure.) One point of the paper is that this gives the apparently first candidate for a dual description of black holes whose horizon size is small compared to the curvature of the ambient spacetime and the idea is to study such small black holes using small dual plasma balls.

There is also some computer simulation involved in doing so, but I don’t really know anything about that.

After Ofer Aharony’s talk Micha Berkooz reported on

M. Berkooz, D. Chung, T. Volansky
**Constraining Modular Inflation in the MSSM from Giant Q-Ball Formation**

hep-ph/0507218

I can only give a very rough impression of that work, since I was not able to really follow much of the details.

The motivation of this work is to see if among the many scalar fields that appear in the minimally supersymmetrically extended standard model (MSSM), some qualify as interesting candidates for the still elusive inflaton field, which is thought to have provided the energy density that drove the suspected inflationary early expansive period of our universe.

Roughly, there are certain such fields which have ‘flat directions’, meaning that the potential of the theory does not change when the value of these fields is changed. Some of them apparently also have an ‘accidental’ $U(1)$-symmetry and hence carry a $U(1)$-charge, called $Q$. Somehow there is an established concept for such a situation, and certain soliton-like solutions to the equations of motions of these fields are known as *Q-balls*.

The authors now investigated in how far such $Q$-balls could provide the right properties to qualify, as I said, as a source of energy density driving cosmological inflation. Unfortunately I cannot honestly report on the details of their findings.