51. Planck 2008: day 4 - Soft wall AdS/QCD
DmitryThe last talk of the 4th day was “Soft wall AdS/QCD” by Tony Gherghetta. The issue is of course desire to find an adequite description of QCD in the regime of strong coupling. One idea that captured everyone’s attention for several years is of course AdS/CFT correspondence.
According to AdS/CFT duality, supergravity on 
describes physics of 
SYM at large ‘t Hooft coupling 
. This is not quite what we need though because:
a) SYM is conformal field theory, while QCD is asymptotically free (coupling becomes stronger in the IR).
b) that QCD we are interested in from the practical point of view actually corresponds to 
.
On the other hand, we can try to take AdS/CFT as zero approximation for description of strong coupling QCD, since the latter is approximately conformal at large energies (I have an impression that the word “approximately” here is more about what one has to believe in rather than something one can consistently check, but I may be wrong). So, we start with 
geometry describing 4d physics of YM CFT at high energies and then somehow introduce a cutoff in 5th dimension in order to induce confinement for the 4d Yang-Mills theory. This cutoff can be either introduced by hands (this is what is called “hard wall AdS/QCD limit”) or dynamically (such as by introducing non-trivial dilaton background - situation of “soft wall AdS/QCD” under present discussion).
As it turns out, in order to reproduce linear Regge trajectories, one has to introduce a dilaton background which is quadratic w.r.t. conformal coordinate 
of AdS:
(1).
The question however is whether it is possible to continue the reverse engeneering process a step further compared to Stephanov et al. and find a selfconsistent solution of supergravity equations such that the gravitational background is and the dilaton background is given by (1).
Tony has introduced a model naturally predicting such a background. The price to pay is that he had to introduce an additional scalar field 
(he wants to identify it with closed string tachyon of non-critical string theory - note that here happens a trick: we don’t want to find consistent 10 dim background of the 
form, but limit the discussion to 5 dim instead) and a very nontrivial potential 
for the dilaton and the field . The effective action for the 5-dim theory is (I am not sure I have to present it here, but I will)
where
.
Looks scary, doesn’t it? ;-)
Since the potential is reverse-ingeneered, it was impossible for me to understand the physical meaning of the potential form (or how it would follow from a stringy model).
Let me finish with a couple of notes:
1) It would be interesting to understand how this model works for the 2D QCD which is exactly solvable - it would correspond to gravity in 
, which is presumably topological (it is a theory of scattering of conical defects produced by the quanta of 
and ).
2) It will be hard to explain the nature of the field and the corresponding terms in the potential from the stringy point of view (we should stick to 10 dim physics in this case). As Tony shows, also has to have a runaway behavior (linear growth with ). I wonder - can be one of the moduli which don’t get stabilized?
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50. Planck 2008: day 4
DmitryAlthough I am back to Helsinki for a week already, let me continue my brief review of Planck 2008 talks :-)
Plenary talks of the 4th day were mostly devoted to unparticles and AdS/QCD, with opening talk by Howard Georgi, inventor of unparticles himself. He was talking about his paper (just released) “An unparticle example in 2D” with Eugene Kats (projector did not work in the beginning of his talk, so he had to talk without transparances or PowerPoint presentation, and I was very much impressed how well he did it).
Let me first remind you what is the buzz concering unpartcles. Imagine some scale invariant matter (that is, spectrum of its excitations is scale invariant). One cannot describe such fields (let us call them ) in terms of particles - the possibility of the latter description would imply that the spectral function of excitations (exp. value of the commutator ![[\Phi(x),\Phi(y)]](http://www.nonequilibrium.net/latexrender/pictures/be53a802d068555eee2b5a8624bfbc27.gif "[\Phi(x),\Phi(y)]")
) has strong peaks at some 
. Positions of the peak would be related to the mass of the “particles”, while widths of the peaks - to the life time of the “particles”. Scale invariant spectral function therefore means that our particles are interacting so strongly, that their notion is undefined.
This scale invariant matter sector can in principle weakly interact with our Standard Model stuff, and its existence can potentially influence SM scattering, in particular, would lead to events of missing energy and momentum in scattering events. Since unparticles are described by CFT, interactions between them and SM are organized as interactions between SM fields and CFT operators with non-trivial scaling dimensions (Georgi calls them Banks-Zaks fields).
After this short introduction, let me go back to Georgi’s talk… He explicitly introduced an example of the 2D theory with unparticles: Thirring model (massless fermions, 4-fermion interaction; the model is exactly solvable, admits bosonization and is nothing else but CFT) with massive vector bosons. The Thirring model with massive gauge bosons turns also out to be exactly solvable. At higher energies the theory approaches free field limit, while in the IR massive vector bosons are integrated out, only fermions survive, so conformal symmetry gets restored (one has Thirring model unparticles).
As a “SM” stuff, Georgi introduces complex scalar field interacting with Thirring fermions through standard trilinear interaction term, so that we can excite unparticles in collisions 
.
The physics of 
scattering turns out to be the following: first of all, there exists the physical scale
where 
is the mass of gauge bosons and 
is their interaction with Thirring fermions. At 
one has energy loss to unparticles, while at 
one can also excite gauge bosons. 
enters the overall cross section pretty much in the same way 
enters cross sections in inclusive QCD processes.
The second talk about unparticles was by John Terning (UC Davis): he discussed AdS/CFT-unparticle interplay. He basically showed that unparticle actions are equivalent to holographic boundary actions for fields in AdS. Clearly, his picture cannot be universal since the class of CFTs is much wider than the class of theories that admit gravity dual.
The talk N3: Antonio Delgado (Notre Dame) has introduced an interaction between Higgs and unarticle stuff of the form
where 
is the CFT operator with dimension 
and tried to figure out how it will influence Higgs physics at LHC. The result of the Higgs-unparticle interplay is the
mass gap in the unparticle continuum and a shift in the Higgs mass. In fact, Higgs state can be above (bound state in unparticle continuous spectrum) or below the mass gap. Also, another isolated state, a mix of Higgs and unparticles (Antonio calls it phantom Higgs), can appear in the spectrum near or below the mass gap. Coupling between phantom Higgs, fermions and gauge bosons are reduced.
During the next talk (”A bound on operator dimension in CFT4 and the hierarchy problem” by Riccardo Ratazzi) I decoupled from the audience and missed it almost completely, but the final talk by Tony Gherghetta has grabbed my attention back. Tony was talking about soft-wall AdS/QCD, the subject that definitely deserves a separate post.
To be continued…
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