## April 27, 2007

Quite some time ago, I wrote about an AdS/CFT-inspired’ model for hadron physics. Despite its crudity, it seems to capture surprisingly well the physics of the low-lying mesons ($\pi$, $\rho$, $a_1$).

It also provides a nice laboratory for studying physics at finite baryon density. The 5D vector field, $\hat{V} = \frac{1}{\sqrt{2 N_f}}Tr(A_L + A_R)$ couples to baryon number. Choosing boundary conditions $\hat{V}_0(z) = A + \tfrac{1}{2} B z^2 +\dots$ corresponds to working at finite chemical potential $\mu_b = A N_c$ and baryon number density $n_b = \frac{1}{24\pi^2} B$

Domokos and Harvey added the 5D Chern-Simons interaction $S_{\text{CS}} = \frac{N_c}{24\pi^2} \int (\omega_5(A_L) - \omega_5(A_R))$ (where $d\omega_5 = Tr F^3$) to the model and found a remarkable effect. At finite baryon density, the 4D effective action contains a term $S = \int d^4x\, \dots +\mu\epsilon^{i j k} (\rho^a_i \partial_j a^a_k + a^a_i \partial_j \rho^a_j)+\dots$ (where $\mu\propto n_b$). Above some critical value of the baryon density, the addition of this term induces a translational- and rotational-invariance breaking condensate of $\rho$ and $a_1$.

At least in this model of Erlich et al, the critical density is in the same ballpark as that of nuclear matter. So, perhaps, this condensate actually forms in neutron stars.

It would be interesting to repeat the calculation in other models, like the Sakai-Sugimoto model, and see how that affects the prediction for the critical density.

Posted by distler at April 27, 2007 10:03 AM

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This reminds me of the phase transition in dense
Skyrmion systems where B=1 Skyrmions undergo
a transition to a chirally symmetric phase phase of B=1/2 objects at a critical density roughly given by the density when nucleons start to overlap.
For example in a paper by Castillejo et al. NPA501,801 it is shown that the B=1/2 objects
are in a fcc crystal. It would be interesting to see the gravity dual of such crystal. However, we should keep in mind that QCD has not gravity dual and the the Skyrme model in not QCD
either.

Posted by: jacobus verbaarschot on April 27, 2007 4:41 PM | Permalink | Reply to this

The transition we are discussing does not involve restoration of chiral symmetry. Regarding the comment that “QCD has not gravity dual” I would say it depends on what you demand of the dual theory. For example, the Sakai-Sugimoto model has exactly the same light degrees of freedom as QCD with massless quarks. Both that model and the AdS/QCD model used in our paper can be used to study QCD at large t’ Hooft coupling and this regime seem to give a reasonably accurate description of QCD physics up to an energy scale which is yet to be determined, but seems to be above 1 GeV.

Posted by: Jeff Harvey on April 27, 2007 5:46 PM | Permalink | Reply to this

Jacques, would you agree that if AdS/QCD, AdS/CMT, now AdS/QHE, and so on… actually work, that they are telling us something about the particular vacuum of string theory that (hypothetically) we inhabit? I know that these calculations are performed using highly supersymmetric theories, and so usually one says that they just offer calculable qualitative models in the same universality class as the condensed-matter phenomena of interest - but if the real world actually consists of strings propagating on a particular geometric background, and if, under the right conditions, they behave like the idealized AdS strings, doesn’t that suggest that some of those AdS phenomena are literally happening?

I find it perplexing that this perspective isn’t raised more often. At Asymptotia, you took the view that e.g. the RHIC plasma isn’t really a 5D black hole, that’s just an approximation… but shouldn’t the success of the approximation imply that it really is something very like a 5D black hole?

To put it another way: At Clifford Johnson’s, you were prepared to say that finite-temperature N=4 SYM really is a 5D black hole. The real world isn’t N=4 SYM, but it is some theory - call it X - and the RHIC plasma is exactly, not just approximately, a phenomenon in X. Mustn’t it therefore be true that the RHIC plasma really is holographically identical to - something? :-)

I brought up such topics with Lubos Motl once and he helpfully reminded me of the Randall-Sundrum picture, where you do have some gravity on the brane and not just in the bulk. That seems like the most straightforward way of “taking AdS/QCD literally” - to embed it in a RS-type realization of the standard model, if such can be found. I said to Lubos, can we throw in AdS/CMT and Kerr/CFT as well, and he said, all these things work in different ways. But it seems to me that if all these various forms of gauge/gravity duality do apply simultaneously to phenomena coexisting in the same world, then one should try to “take them literally” all at the same time. QCD, condensed matter, astrophysical black holes, that’s a big chunk of the real world right there. There’s more than one black hole in the real world, so first of all we need to have a CFT dual for a multi-black hole state, and then we need to embed the standard model fields in that somehow… that’s my thinking, but I’m not yet at the stage where I can try to implement this program.

Posted by: Mitchell Porter on August 12, 2010 5:19 AM | Permalink | Reply to this

Jacques, would you agree that if AdS/QCD, AdS/CMT, now AdS/QHE, and so on… actually work, that they are telling us something about the particular vacuum of string theory that (hypothetically) we inhabit?

The RHIC plasma (to pick one of your examples) is pretty far from the vacuum.

To put it another way: At Clifford Johnson’s, you were prepared to say that finite-temperature N=4 SYM really is a 5D black hole.

I was prepared to say it, because it’s true.

The real world isn’t N=4 SYM, but it is some theory - call it X - and the RHIC plasma is exactly, not just approximately, a phenomenon in X. Mustn’t it therefore be true that the RHIC plasma really is holographically identical to - something? :-)

Sorry, but that doesn’t follow.

There’s a very particular class of field theories – characterized by the fact that their short-distance behaviour is governed by a nontrivial interacting SCFT (of a certain sort, that I’m not going to try to precisely state) – which have holographic duals. The beauty and power of universality is that theories, with the same long distance behaviour, can be very different at short distances.

So you can use one of these holographic theories to describe the same long distance physics as a theory with radically different short-distance physics. (In AdS/CMT, consider that we are modeling the long-distance non-Fermi-liquid behaviour of systems which, at short distances, have atoms ‘n crap.)

I brought up such topics with Lubos Motl once and he helpfully reminded me of the Randall-Sundrum picture, where you do have some gravity on the brane and not just in the bulk. That seems like the most straightforward way of “taking AdS/QCD literally” - to embed it in a RS-type realization of the standard model, if such can be found.

All of the Type-II/M-theory compactifications (including F-theory) which have chiral matter and nonabelian gauge fields have the feature that the latter are localized on (possibly singular) submanifolds of the compactification manifold, whereas gravity lives in the bulk.

In the presence of large warping, the local physics in the vicinity of those submanifolds looks very much like AdS/CFT. But – in the F-theory compactifications proposed by Vafa and collaborators (to pick my favourite example) – the details are rather different. There’s no AdS dual for the 8-dimensional gauge theories that arise on 7-branes.

Posted by: Jacques Distler on August 12, 2010 3:21 PM | Permalink | PGP Sig | Reply to this

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