Quark Mass in Holographic QCD

1. 30th April, 2007 @ Galileo Galilei Institute, Florence Quark Mass in Holographic QCD Koji Hashimoto (RIKEN) arXiv/0803.4192(hep-th) w/ T.Hirayama, Feng-Li Lin （National Taiwan Normal U） and Ho-Ung Yee （ICTP Trieste） Note : Significant overlap with [Aharony, Kutasov 0803.3547]

3. 1. Problem of Sakai-Sugimoto Problem Cause Solution Benefit

4. Sakai-Sugimoto model Best model of holographic QCD : Sakai-Sugimoto model Massless QCD on D4 Gauge/Gravity (AdS/CFT) Correspondence Gravity Dual Composite operator states in the bulk

5. Problem of the Sakai-Sugimoto model Quarks are massless! String QCD L-Flavor D4-D4 Gluon D4-D8 L-quark D4-D8 R-quark R-Flavor Color Quark mass is important in QCD…… Explicit vs Spontaneous chiral sym. breaking Chiral condensate GOR relation between pion and quark mass Strange dynamics

6. Causes of the problem (a) There is no room to make the D8s separate from D4 (b) L and R quarks live on different locations in 10dim. L Quark mass term : R

7. Our Solution to the problem (1) Worldsheet instanton Yukawa interactions in string phenomenology Dp Dp Dp = (2) Extended Technicolor Techni-sector QCD sector techni-quarks “W-boson”

8. Our results We derive GOR relation Chiral condensate Chiral lagrangian Low energy sector of the SS model is drastically refined! Importance (future directions) Strange physics Finite temperature / finite density QCD

9. Plan of today’s talk 1. Problem and Our Solution 2. Brief Review of Sakai-Sugimoto 3. Quark mass, Pion mass 4. Chiral condensate, Flavor dep. 6 slides 5 slides 5 slides

10. 2. Sakai-Sugimoto : Review

11. AdS/CFT：　Equivalence of two ways to describe D-branes [Maldacena(97)] QCD Gravity -dual Open string （gauge theory） Closed string （gravity） Holographic QCD Closed string in blackbrane background of N D3-branes Low energy effective action of open strings on N D3-branes 10 dim. supergravity in curved backgrounds 4dim. gauge theory Corresp.

12. Sakai-Sugimoto model(hep-th/0412141) Open string side (D-branes) ・　Nc D4-branes wrap with radius Gauginos satisfy anti-periodic boundary condition  Massless gluonsat low energy, SU(Nc) gauge [Witten] ・　Nf D8 intersecting D4s  Nf massless L-quarks ・　Nf D8 intersecting D4s  Nf massless R-quarks Massless QCD is brane-engineered at low energy D8 x D8 gauge group = Chiral symmetry

13. Closed string side (gravity) D8s : probe (approximation valid at ) Near horizon geometry of black 4-brane solution on which fermions satisfy the anti-periodic b.c. is [Witten] Geometry truncated at  D8 and D8 are connected  Spontaneous Chiral sym. br.

14. Once the correspondence is applied… ＝ D8 D4 ・ D8 → bound states of quarks（Mesons, Baryons） KK modes of gauge fields on the D8 → Meson D8-brane action → Chiral lagrangian ・ gravity → bound states of gluons（Glueballs）

15. Meson sector in the SS model D8-brane action on the curved background Induced metric: z Redefinition of coordinates： KK modes of Vector mesons A KK mode of  massless Pion

16. Going to gauge and integrating D8-brane action = Chiral lagrangian Sugra parameters are

17. 3. Quark Mass, Pion Mass

18. Extended technicolor  quark mass Technicolor sector : QCD Technicolor Mediator Quark mass Techni-quark W-induced 4-Fermi Condensation

19. Brane configuration of the Technicolor ref. [Hirayama, Yoshioka (07)] Technicolor sector || Additional D4s Strongly coupled Technicolor sector || Another throat

20. Worldsheet instanton Double-line = Worldsheet instanton

21. Quark mass Worldsheet instanton W-boson mass : Quark mass :

22. Pion mass Gravity dual has 2 throats  Non-trivial 1-cycle on the D8-brane Boundary coupling to D8 gauge field b.g. Worldsheet instanton Chiral lagrangian GOR relation

23. Chiral Condensate, Flavor Dependence

24. D6 instead of the D4’ Difficulties in the introduction of the D4’ : Joining two gravity solutions? Decoupling of the overall NG boson? Coefficient c to compute chiral condensate? We introduce a D6 ending on D8 and D8 intead of the D4’ D6 A lot simpler!

25. Virtue of the D6 D6 is a probe. No need of new b.g. D6 is given as a spike solution of the D8 DBI. D6 spike D6 charge is magnetic (1,-1) under the chiral symmetry :  Explicit breaking of the chiral symmetry Worldsheet instanton for the quark mass is given in flat spacetime 

26. Chiral lagrangian Worldsheet instanton looks same. D6 spike D4 throat : effective coupling

27. 2D8 Chiral condensate, flavor dependence D6 2D8 On each D8, D6 ends Standard chiral lagrangian

28. Numerics ( just for illustration ) Pion / quark mass From pion decay constant and rho meson mass, We substitute , Cf) Experiments : Chiral condensate Cf) Lattice :

29. 5. Conclusions

30. Our solution to the massless quark problem Extended technicolor + worldsheet instanton  Quark mass, pion mass GOR relation We have derived Chiral condensate Chiral lagrangian Low energy sector of the SS model is refined!

31. Relation to previous attempts Tachyon condensation (Higgs mechanism) Quark mass [Casero, Kiritsis, Peredes (07)] [Bergman, Seki, Sonnenschein (07)] [Dhar, Nag (07)] D8-D8 string : “tachyon” Gauge invariant term Difficulty : Tachyon action? … No consistent truncation?

32. “Tachyon” picture and our solution Tachyon condensation = partial annihilation of D8D8 (non-normalizable mode of “bulk tachyon” quark mass) The same worldsheet instanton gives the quark mass = Higgs mechanism and technicolor are s-t channel dual to each other! =

33. Future directions Strange physics, K/pi mass difference …. 2 instantons Finite temperature / finite density QCD Running charm in QGP? Deconfinement transition temperature? More precise evaluation of the instanton amplitudes Vector meson mass?