Extracting numbers from AdS/QCD
This Wednesday's seminar at CTP was given by Emanuel Katz of Boston University (see him here). He talked about his recent work on AdS/QCD correspondence, published in hep-ph/0501128. The main program here is to find a 5D string theory such that QCD is its induced theory on the 4D boundary of this bulk. So far nobody could came up with such a theory. QCD has a very rich structure with asymptotic freedom, chiral symmetry breaking and many particle fields. Unless you came up with the right matter content and exact SU(3) symmetry there is no hope that you can have reasonable calculations for low energy. (Low energy is interesting because high energy QCD is easy to due to asymptotic freedom.)
Katz and his collaborators took a simpler and different approach. Instead of finding a full fundamental theory, they tried to find a few relevant terms in the bulk, fix their coefficients by QCD data and compute other data and see if there is anything matches (which is not very likely a priori). They took an AdS space with a boundary where we live. Fifth dimension in the bulk, corresponds to the energy scale of the interactions on the boundary. As you move away from the boundary energy scale gets smaller (length scale gets larger). So if you want to study confinement you need to study the region near the boundary. In their model this is done by putting another brane parallel to the boundary as an infrared cut-off and study the region in between. Physics is imposed by the boundary conditions on the 'infrared brane'. There are four free parameters in the Lagrangian which are set by number of colors and three experimental values like the rho meson mass, the pion mass, and the pion decay constant. Surprising thing is after building this simple but very unrealistic model they can calculate many other experimental parameters very accurately (within %10 in most of the cases). He showed additional results with strange quark in the talk and even they are still very good (within %30). Actually this is better than the first versions of computationally intensive lattice-QCD.
I always thought that even if they find a dual theory for QCD, it would be much more complicated and will not be practical for anything beyond intellectual joy. But this work made me step back and take a second look. May be there is something here.
Even more important question is whether it has a fundamental meaning or not. Spring-mass system and an LC circuit have dual theories (actually same theories with different coordinate names). But it does not mean that one is made out of the other. Are we really living on a brane and is standard model just a projection of a (5+n)D theory? Probably I will never learn the answer.
Update: I just saw that Jacques Distler has a slightly more technical review of this paper.
Katz and his collaborators took a simpler and different approach. Instead of finding a full fundamental theory, they tried to find a few relevant terms in the bulk, fix their coefficients by QCD data and compute other data and see if there is anything matches (which is not very likely a priori). They took an AdS space with a boundary where we live. Fifth dimension in the bulk, corresponds to the energy scale of the interactions on the boundary. As you move away from the boundary energy scale gets smaller (length scale gets larger). So if you want to study confinement you need to study the region near the boundary. In their model this is done by putting another brane parallel to the boundary as an infrared cut-off and study the region in between. Physics is imposed by the boundary conditions on the 'infrared brane'. There are four free parameters in the Lagrangian which are set by number of colors and three experimental values like the rho meson mass, the pion mass, and the pion decay constant. Surprising thing is after building this simple but very unrealistic model they can calculate many other experimental parameters very accurately (within %10 in most of the cases). He showed additional results with strange quark in the talk and even they are still very good (within %30). Actually this is better than the first versions of computationally intensive lattice-QCD.
I always thought that even if they find a dual theory for QCD, it would be much more complicated and will not be practical for anything beyond intellectual joy. But this work made me step back and take a second look. May be there is something here.
Even more important question is whether it has a fundamental meaning or not. Spring-mass system and an LC circuit have dual theories (actually same theories with different coordinate names). But it does not mean that one is made out of the other. Are we really living on a brane and is standard model just a projection of a (5+n)D theory? Probably I will never learn the answer.
Update: I just saw that Jacques Distler has a slightly more technical review of this paper.
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