2. The fast life of holographic mesons Aninda Sinha Perimeter Institute, Canada. with Robert Myers arXiv:0802.nnnn Quark Matter 2008, Jaipur, India

3. PLAN I) Motivation and setup II) Spectral functions of holographic mesons, decay widths III) Conclusion

4. I) Motivation and setup Behaviour of strongly coupled QCD is of interest to RHIC and early universe cosmology. Unfortunately, theoretical tools are rather limited. Recently, string theory tools involving gauge/gravity duality have been used to gain some insight into the nature of this interesting regime. limitation: large N C and large ’t Hooft coupling

5. AdS/CFT relates N=4, d=4 supersymmetric Yang Mills theory and its deformations to a theory of gravity in Anti-de-Sitter space (a space with negative cosmological constant) arising as a solution to d=10 superstring theory. In particular, the effective gravity theory is on AdS 5 x S 5. The strongly coupled regime of the gauge theory is mapped into a weakly coupled gravity theory. Idea is to try and do calculations using the gravity theory to gain some insight into the strong coupling region of the gauge theory.

6. QCD N=4 SYM confinement, discrete spectrum, scattering,.... conformal, continuous spectrum, no S-matrix, SUSY,.... very different !! T=0 strongly-coupled plasma of gluons & adjoint matter deconfined, screening, finite corr. lengths,... strongly-coupled plasma of gluons & fundamental matter deconfined, screening, finite corr. lengths,... T>T C T>>T C quite similar !! cf runs to weak coupling remains strongly-coupled very different !!

7. Baryon density n causes brane to reach horizon q Free quark 1) Start with black hole in AdS to get finite temperature, have deconfined adjoint matter II) Add D-brane to get flavour RECIPE FOR HOLOGRAPHIC QUARK GLUON SOUP [Aharony, Fayazuddin, Maldacena; Karch, Katz; Kruczenski, Mateos, Myers, Winters] III) String falls into black hole and melts mesons IV) Mass of meson, decay controlled by baryon density and geometry of D-brane (quark bare mass and condensate depend on these)

8. SPECIFIC QUESTION: What can we say about the masses and lifetimes of holographic mesons at strong coupling? What is the nature of the spectral functions with changing momentum and other parameters? BROADER QUESTION (for the future): Do these features have anything in common with Lattice data and/or real world?

9. Spectral functions from AdS/CFT F,G,R are functions of r which is the holographic direction. Spectral function is defined as For us is large. Can recast in terms of an effective Schrodinger equation

10. Bound state Horizon Holographic direction Behaviour of effective holographic potential with changing momentum

18. II) Spectral functions and widths n q = 0 0.06 0.15 0.25 Quasiparticles

19. n q = 0.25

20. Speed limit from spectral peaks [Liu, Rajagopal, Wiedemann; Mateos, Myers, Thomson; Ejaz, Faulkner, Liu, Rajagopal, Wiedemann; Athanasiou, Liiu, Rajagopal; Myers, AS] Real part of quasinormal frequency n q = 0.25

21. v max = 0.9954 v max = 0.6512 v max = 0.3427 Dispersion relations for first 3 peaks for different parameters At same temperature, higher v max means higher bare quark mass. Equivalently, keeping bare quark mass fixed, higher v max means lower temperature.

22. Widths as function of momenta [Myers, AS] V=0.34 V=0.65 V=0.99 Location where effective potential has no minima

23. Conclusion Holographic methods suggest finite velocity effects in the dispersion relations. Arise quite generally due to red-shift in the dual gravity picture. Finite baryon density induces quasiparticle widths to grow dramatically with momenta. Can be quite general but needs further investigation. THANKS FOR LISTENING

26. Mesons: lowest lying open string states are excitations of the massless modes on D7-brane: vector, scalars (& spinors) their dynamics is governed by usual worldvolume action: free spectrum: expand action to second order in fluctuations solve linearized eq’s of motion by separation of variables V eff r discrete spectrum Kruczenski, Mateos, RCM and Winters (hep-th/0304032) Mesons stable

27. entropy density: Reminder about large N counting: counts # of d.o.f. entropy density: counts # of d.o.f. in our limit, thermodynamics dominated by adjoint fields; we are calculating small corrections due to fundamental matter these dominate over quantum effects, eg, Hawking radiation,

28. Brane entropy: 1 st order phase transition Transition temperature:

29. Kobayashi, Mateos, Matsuura, RCM & Thomson [hep-th/0611099] Mateos, Matsuura, RCM & Thomson [arXiv:0709.1225];..... Need an extra dial: “Quark” density electric field lines can’t end in empty space; n q produces neck D7-brane gauge field: asymptotically (ρ→∞): BH embedding with tunable horizon