1. Topological current effect on hQCD at finite density and magnetic field Pablo A. Morales Work in collaboration with Kenji Fukushima Based on Phys. Rev. Lett. 111, 051601 (2013)

2. Outline INTRODUCTION QCD Phase Diagram. AdS/CFT correspondance and holography The phase diagram according to the Sakai Sugimoto model... And then introducing finite B? Spatially Inhomogeneous phases The Inhomogeneous phase according to the Sakai Sugimoto model... And then introducing finite B? Conclusions and Future Work (on the way)

3. Quantum Chromodynamics (QCD) [Fukushima-Sasaki 2013] Lattice QCD Perturbative QCD

4. All contributions from the current-current interaction corresponding to the underlying symmetry must be included, not only (even when gauge fields are integrated out) Crucial even at mean field approximation to liquid-gas phase transition of dense quark matter In order for Effective Field Theories to give an accurate description...

5. Complications in the QCD phase diagram go beyond inclusion of finite density The inclusion of B in this picture is imperative: Chiral Magnetic Spirals Magnetic Catalisys Chiral Magnetic/Separation Effect Phenomenological and Experimental Theoretical side momentum spin Quark Gluon Plasma

6. Magnetic field in the QCD phase diagram Magnetic catalisys has been observed in effective field theories and lattice QCD (although with unphysical masses) Chemical Potential Chiral Boundary Chirality is locked with the spin So if we apply a magnetic field momentum spin

7. Just like vector-type interactions, even at mean field level the axial-vector interaction has a nonzero contribution, however it has been assummed to have no effect on the structure on the phase diagram However, it is necessary to address on one important physical effect that has been overlooked up until now, that is, the inevitable formation of the topological current!

8. Towards a Holographic Representation of QCD The Sakai-Sugimoto model

9. The Gauge/Gravity Duality Weak Gravity Strong Gravity Strong Coupling Weak Coupling Duality difficult! easy! CFT N=4 Super Yang Mills The strong coupling limit (hard to solve) in gauge theories happens to be dual to the weak gravity in string theory First step to QCD

10. 0123456789 OOOOO Minkowski Compactify U Holographic dim Properties: 1.SUSY, Conformal 2.No Chiral Symmetry 3.No Confinement Towards a holographic realization of QCD

11. Confined Deconfined

12. 0123456789 OOOOO OOOOOOOOO Adding Flavor Close to QCD! 1.SUSY broken 2.Confinement 3.Chiral Symmetry Breaking

13. Adding Flavor: Chiral Symmetry Breaking L L

14. Holographic QCD phase diagram

15. [Bergman Lifschytz Lippert 2009] Holographic QCD phase diagram...Still a question remains

16. Magnetic field in hQCD and topological current DBI Action Chern-Simons Action Flavor sector action Equations of motion Asymptotic solutions

17. [Preis, Rebhan, Schmidt 2013] Topological current in the homogeneous chiral surface Presence of quark matter neutron stars!

18. Spacially modulated region in the phase diagram

19. Spatially Modulated Phases Inhomogeneous! Effective Chiral models PNJL... Lattice results Chiral Spirals [Bassar-Dunnes-Kharsheev] [Hidaka-Kojo] If the system the system at zero density has a condensate Then the rotated system has the same condensate This may be the case at high densities (Fermi surface realizes a pseudo (1+1)-dim system)

20. What should we expect at finite B? Reduces the system effectively to a (1+1) dimensions. Axial current is strengthened by strong B Favors spiral configuration Spatial Inhomogeneity + Topological axial current Sakai Sugimoto model hQCD Unperturbative QCD method

21. Inhomogeneous phase in hQCD EOM decoupled in terms of dual fields Sketch of calculations

22. [Ooguri-Park 2010] A minimum value for the Chern-Simons coupling constant (at which instabilities can be found) can be determined analitically However the corresponding critical density has to be found numerically [Chuang-Dai-Kawamoto -Lin-Yeh 2011] This instability can be predicted to occur in QGP...Then again what happens at finite B?!

23. Addition of a magnetic field into the picture results into the breaking of rotational invariance of the EOM corresponding to the fluctuations and thus the system cannot be trivially decoupled in terms of the dual field as usual. So we solve numerically, from the condition that these fluctuations correspond to normalizable modes [Fukushima-Morales 2013]...presence of current changes results drastically!

24. [Fukushima-Morales 2013] Surprising results! However... Shrinking of Inhomogeneous phase!

25. Conclusions/Future work Holographic QCD provides us the means to study unpertubatively the effect of the topological axial current in the phase diagram The role played the topological current in the phase diagram is critical to its homogeneous part and inhomogenous phase as well.....(What happens in other effective chiral models? Universal Feature?) Could this Inhomogeneous phase be the dual of the ground state in QCD... (Chiral Spirals?)

26. Inhomogeneous Phases [Ooguri-Nakamura 2011] When considering coupling to gravity, although the stability condition is modified in more complicated geometries, tachyonic modes can be found Bottom-up approach