On the existence of a holographic description of the LHC quark–gluon plasmas

Abstract

Peripheral collisions of heavy ions can give rise to extremely intense magnetic fields. It has been suggested that these fields might invalidate the holographic description of the corresponding quark-gluon plasmas, assuming that these can be modelled by strongly coupled field theories. In the case of the plasmas produced in collisions at the RHIC facility (including in the beam energy scans), it is known how to deal with this problem: one has to take into account the large angular momenta generated in these plasmas, and the effects of the baryonic chemical potential. But this does not work for the plasmas produced in peripheral collisions at the LHC. However, these results neglect some (less significant) aspects of bulk physics; could it be that the problem is resolved by taking into account these lower-order effects? Here we use a bulk dilatonic field (fully compatible with boundary data, as well as with the asymptotically AdS character of the bulk geometry) as a model of these effects, and show that this is unlikely to be the solution. Thus, the existence of a consistent holographic description of the most extreme LHC plasmas remains open to question.

Holography of the QGP Reynolds number

“…On the other hand, for maximal LHC data, far larger values of the angular momentum were required to ensure that S E is never negative in that case; similarly, we found in [71] that, for these data, a dilaton coupling at least as large as α ≈ 0.284 is needed. Thus, the dilaton coupling does mimic the effect of angular momentum for our purposes 17 .…”

“…whether the required value of the angular momentum parameter is realistic in the case of collisions with maximal magnetic fields. We found in [63] (see also [71]) that this is definitely not a problem in the case of the RHIC plasmas, but that it could be in the LHC case. Since the phenomenon in which we are interested here appears already even at relatively low values of the magnetic field, we will not take a stand on this issue here.…”

How does the Quark-Gluon Plasma know the collision energy?

“…Gauge-gravity models of jet quenching are of course well known [35,36], and such models also exist which take into account the effect of the magnetic field [37]. Here we will use a much more basic "minimal" model [38,39] in which the bulk geometry is that of a magnetically charged dilatonic asymptotically AdS thermal black hole 3 . We stress again that there is no reason to expect, over the relatively narrow range of magnetic field values being considered here, any close agreement with the findings of [6][7][8]; indeed it is not clear that the holographically computed values of K will even change in the correct direction (smaller for the LHC plasmas, by a factor of around 2 or 3, or perhaps a little more for the 5.02 TeV collisions).…”

“…For the purposes of this work, the reader may regard the presence of the dilaton as essentially a technical matter, required (when magnetic fields are extremely strong relative to the squared temperature) in order to ensure that the bulk system is mathematically consistent within string theory 5 . The form taken by this mathematical consistency condition in the present application is discussed in detail in [46,38,39]. The value of the coupling α is chosen to be the minimal value that results in this condition being satisfied.…”

“…As explained above, this means that we will consider three values for eB ∞ : eB ∞ ≈ 60 m 2 π , eB ∞ ≈ 6 m 2 π , and eB ∞ ≈ 0.6 m 2 π . These data allow us to compute α ≈ 0.34, α ≈ 0, α ≈ 0 for the three respective cases 7 , after the manner of [38,39]. We can now solve (9), (10), and (11) for P * , r h , and M * in each of the three cases, and again equation (12) yields three values for s P LHC /ǫ; note that, by construction of course, ǫ is the same throughout these computations.…”