Holographic QCD model from heavy quark potential QCD new frontiers 2010, March 11 th 2010, YITP, Kyoto Mei Huang Institute of High Energy Physics, CAS Theoretical Physics Center for Science Facilities, CAS

2 Content I.Introduction II.Holographic QCD models III.Our model & heavy quark potential IV. Conclusion and Discussion Song He, Mei Huang, Qi-shu Yan, in preparation

3 QCDQCD ? String theory, quantum gravity Non-Abelian gauge theory AdS/CFT conjecture If it’s true for any gauge theory Then what ’ s the dual string theory of QCD? Question: Is it possible to find a string theory dual to QCD? I.Introduction

4 First step, is it possible to find a 5D holographic model of QCD? Metric structure of holographic QCD (5D) QCD Dp-Dq system in type-II superstring theory (10D) What we can do: extract a workable holographic QCD model from the real world Leave the task of deriving the holographic QCD model to string theorists

5 II.Holographic models Bottom-up models: hard-wall AdS5 model soft-wall AdS5 model: quadratic dilaton model Andreev model: negative quadratic dilaton model back-reaction model model resembling QCD running coupling Top-down models: SS model, Dp-Dq model…

6 Hard-wall AdS 5 model: Lowest excitations: 80-90% agreement with Exp. higher excitations: no Regge behavior

7 Introduce a dilaton field to restore Regge behavior Soft-wall AdS 5 model or KKSS model

8 O. Andreev, hep-ph/ Andreev’s model: quadratic correction KKSS model (effectively): Heavy quark potential

9 C.D. White, hep-ph/ Back-reaction model: higher-order corrections J.P.Shock, F.Wu, Y.L.Wu and Z.F.Xie, hep-ph/

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11 H.J.Pirner, B.Galow, arXiv: Pirner-Galow model: resemble QCD running coupling

12 B.Galow, E.Megias,J.Nian,H.J.Pirner, arXiv: Pirner-Galow model: produce heavy quark potential very well

13 Pirner-Galow model: however, unstable dilaton potential B.Galow, E.Megias,J.Nian,H.J.Pirner, arXiv:

14 Deformed warp factor in Pirner-Galow model UV: IR: III Construct holographic QCD model from heavy-quark potential

15 Dp-Dq model S. He, M. Huang, Q. S. Yan, Y. Yang,

16 S. He, M. Huang, Q. S. Yan, in preparation Our holographic model: can be either positive or negative

17 Calculate heavy quark potential (standard)

18 heavy quark potential expanded at R=0 1, Coulomb part is determined by string tension 2, Quadratic and logarithmic contributions to the linear part compete with each other

19 Gravity solution of the metric Einstein-dilaton equations:

20 Gravity solution of the metric

21 1, Only quadratic corrections: cannot produce HQ potential

22 which is extracted from Pirner-Galow metric, can produce HQ potential, but the dilaton potential is unstable

23 with only logarithmic contribution, can produce HQ potential, and the dilaton potential is also stable

24 Stability analysis R(z)

25 More compact model with less parameters: two scales: L (AdS5 radius) z_IR (IR cut-off)

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Summary I.With only quadratic correction in the deformed warp factor, it’s impossible to fit the heavy quark potential. II.With only logarithmic correction, it can fit the heavy quark potential very well. III. The stability analysis of the dilaton potential constrains 0<c0<0.4. IV.More observables needed to constrain the model further. V.Work in progress (bottom-up): Heavy quark dissociation temperature, Polyakov loop, QCD EOS … VI. Work in progress (top-down): try to derive the model from top-down.

28 Welcome to KITPC program “AdS/CFT and Novel Approaches to Hadron and Heavy Ion Physics” From to , KITPC, Beijing, China