Holographic QCD and pion mass Akitsugu Miwa Institute

Holographic QCD and pion mass Akitsugu Miwa (Institute of Physics, Univ of Tokyo, Komaba) based on JHEP 0706: 020 [hep-th/0703024] with Koji. Hashimoto, Takayuki. Hirayama

Holographic QCD approach: String/Gauge duality ⇒ strong coupling QCD steps in the Holographic QCD: 1. D-branes in flat spacetime open string fluctuation ( weak coupling picture ) ⇒ low energy QCD 2. large # of D-branes ⇒ SUGRA solution ( strong coupling picture ) “Ad. S/CFT conjecture” classical gravity on the near horizon region ⇒ understanding of strong coupling QCD

Sakai-Sugimoto model weak coupling picture: [Sakai, Sugimoto 04] 4 dim QCD S 1 • separated D 8/anti-D 8 ⇒ exact chiral symm. strong coupling picture: meson • connected D 8/anti-D 8 ⇒ spontaneous chiral symm. breaking near horizon • massless pion flat

deformation of SS-model (weak coupling picture) SS-model: = [Callan, Maldacena (98)] [Constable, Myers, Tafjord (01)] deformation: = • connected D 8/anti-D 8 ⇒ only • massive quarks (expectation) S 4 instanton ( from R 4 instanton ): ⇒ symm.

strong coupling picture 1: meson spectrum open string fluctuation: KK-reduction: ( x , U , S 4 ) ⇒ ( x ) • S 4 -integral: only the lowest modes • -integral: mode expansion, diagonalize c. f. ) in the SS-model: pion meson spectrum: vector meson

strong coupling picture 2: chiral perturbation low energy effective Lagrangian of QCD: pion mass term chiral perturbation from D-brane model: • identify and in our model • rewrite the D-brane action using pion mass term corresponding deformation of QCD: ⇔

Summary and Discussion motivation: deformation of SS-model: connect D 8/anti-D 8 in flat spacetime ⇒ explicitly broken chiral symm. separate D 8 from D 4 ⇒ quark mass (expectation) results: meson spectrum: • non-zero pion mass • no effect on vector meson spectrum chiral perturbation: • no quark mass term discussion: why no quark mass term ? : thin throat