Topological c urrent effect on hQCD at finite density and magnetic field

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) LatticeQCD Perturbative QCD ? [Fukushima-Sasaki 2013]

4. In order for Effective Field Theories to give an accurate description... • All contributions from the current-current interaction corresponding to the underlying symmetry must be included, not only (even when gauge fields are integrated out) • Effects coming from vector-current , which gives rise to a density-density interactions, have been vastly studied in the phase diagram. Crucial even at mean field approximation to liquid-gas phase transition of dense quark matter

5. Complications in the QCD phase diagram go beyond inclusion of finite density The inclusion of B in this picture is imperative: Phenomenological and Experimental Theoretical side • Early Universe • Neutron stars, Magnetars G • QGP in heavy ion collisions • Chiral Magnetic Spirals • Magnetic Catalisys • Chiral Magnetic/SeparationEffect spin Quark Gluon Plasma G momentum

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

7. 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! 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

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

9. The Gauge/Gravity Duality difficult! easy! Duality Weak Gravity Strong Gravity Strong Coupling Weak Coupling • The strong coupling limit (hard tosolve) in gauge theories happensto be dual to the weak gravity instring theory CFT N=4 Super Yang Mills Type IIB String Theory on First step to QCD • (Large ) limit of QCD. A theoryof gluon degrees of freedom

10. Towards a holographic realization of QCD • Properties: • SUSY, Conformal • No Chiral Symmetry • No Confinement =4 Super Yang Mills U Minkowski Compactify Holographic dim

11. Deconfined Confined

12. Adding Flavor Receipt: Add Flavor branes and Distributed througout • Close to QCD! • SUSY broken • Confinement • Chiral Symmetry Breaking

13. Adding Flavor: Chiral Symmetry Breaking When the two branes and are connected in the interior of the bulk space. Fields do not transform independently L L

14. Holographic QCD phase diagram

15. Holographic QCD phase diagram • ! • Second order PT to nuclear matter • Constant ...Still a question remains [Bergman Lifschytz Lippert 2009]

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

17. Topological current in the homogeneous chiral surface • Presence of topological current results in restoration of chiral symmetry at Presence of quark matter neutron stars! • Whereas its absence results remains brokenFull chiral surface (ongoing reseach) [Preis, Rebhan, Schmidt 2013]

18. Spacially modulated region in the phase diagram

19. Spatially Modulated Phases Inhomogeneous! Lattice results Effective Chiral models PNJL... Chiral Spirals 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) [Bassar-Dunnes-Kharsheev] [Hidaka-Kojo]

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

21. Inhomogeneous phase in hQCD Sketch of calculations EOM decoupled in terms of dual fields • Imaginary dispersion relation Instability • Differential Equation dependant onof

22. This instability can be predicted to occur in QGP 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 [Ooguri-Park 2010] [Chuang-Dai-Kawamoto -Lin-Yeh 2011] ...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 ...presence of current changes results drastically! phase is enhanced with [Fukushima-Morales 2013]

24. dimensional reduction more spirals! However... Surprising results! Shrinking of Inhomogeneous phase! Topological current Less spirals! [Fukushima-Morales 2013]

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 Chern-Simmons term in 5 dimensions can turn the Maxwell theory tachyonic through a magnetic field When considering coupling to gravity, although the stability condition is modified in more complicated geometries, tachyonic modes can be found Bottom-up approach [Ooguri-Nakamura 2011]