## Saturday, August 11, 2007 ... //

### Sakai-Sugimoto model: papers on Friday

The Sakai-Sugimoto model is arguably the most accurate string-theoretical holographic realization of the "real" QCD.

You may see an explanation by Jacques Distler but let me say a few words.

Holographic QCD: the brane setup

Take a stack of D4-branes stretched in the directions 0,1,2,3,4. You finally only want 3+1 dimensions so you compactify the direction 4 on a circle. You want to end up with a SUSY-breaking QCD even for the vector multiplets in the adjoint (44-strings), so you impose antiperiodic, Scherk-Schwarz boundary conditions on the circle number 4.

To find quarks, you add codimension-one D8-branes and anti-D8-branes localized in the direction number four and take a limit in which the D8-branes are probes. The number of D8-branes equals the number of flavors, and so does the number of anti-D8-branes. Take the near-horizon limit near the intersection, and this is your holographic dual of QCD.

The cutest aspect of the model is the explanation of the chiral symmetry breaking. The "U(Nf) x U(Nf)" symmetry of the D8-branes and anti-D8-branes is broken to the diagonal symmetry simply because the D8-branes bend and continuously connect to their anti-partners. This kind of a geometric representation of the other non-geometric effect is more than just a psychological visualization trick: it is a part of a model that may exactly reproduce QCD.

News

On Friday, Burrington, Kaplunovsky, Sonnenschein find a non-obvious cancellation of Dirac-Born-Infeld and Chern-Simons terms of the D8-brane action and a backreaction that prevents the mesons from becoming tachyonic.

Also, Rozali, Shieh, Van Raamsdonk, and Wu study the model at a non-zero chemical potential and argue that the nuclear matter phase must be non-uniform, potentially giving a geometric explanation for the "chiral density wave" instability of the quark Fermi surface for a large numbers of colors and a high chemical potential.