1. Tigran Kalaydzhyan Spring School on Superstring Theory and Related Topics 28 March - 05 April 2011. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. P.Buividovich, M.Chernodub, D.Kharzeev, T.K., E.Luschevskaya, M.I.Polikarpov, PRL 105 132001 V. Braguta, P. Buividovich, T. K., S. Kuznetsov, M.I. Polikarpov, PoS LATTICE2010 190 P. Buividovich, T. K., M.I. Polikarpov (in preparation) Local CP-violation in quark-gluon plasma: a lattice study. DESY THEORY WORKSHOP September 27 – 30, 2011 Cosmology meets Particle Physics: Ideas & Measurements DESY Hamburg, Germany

2. Topological charge density

3. Chiral Magnetic Effect Abelev et al. (2009-2010), Kharzeev, McLerran, Warringa (2007) Excess of positive charge Excess of negative charge

4. Lüscher and Weisz (1985), see also Lepage hep-lat/9607076 Step 1: Lattice action

5. ● Heat bath for SU(2)‏ ● Using the standard algorithm for each subgroup. Cabibbo & Marinari (1982)‏ Overrelaxation. Adler (1981)‏ Cooling (smearing) for some particular cases. DeGrand, Hasenfratz, Kovács (1997) Step 2: Monte Carlo

6. Buividovich, Chernodub, Luschevskaya, Polikarpov (2009) Neuberger overlap operator (1998) ‏ Фермионы Фермионы Step 3: Fermions & B-field

7. Chirality fluctuations (T<T c )‏ Current fluctuations (T<T c )‏ Fluctuations of chirality Fluctuations of chirality

8. Current fluctuations (T<T c )‏ Current fluctuations‏ Current fluctuations‏

9. Current-current correlator CONFINEMENT DECONFINEMENT (T=350 MeV)

10. ... and its spectral function Conductivity Meson masses

11. Electrical conductivity P.V. Buividovich, M.N. Chernodub, D.E. Kharzeev, T.K., E.V. Luschevskaya, M.I. Polikarpov (2010)

12. What does it mean? There are similar effects for T > T c and thus the local CP-violation is present in the both confinement and deconfinement phases Above T c vacuum is a conductor Below T c vacuum is either an insulator (for B = 0) or an anisotropic conductor (for strong B) This supports the idea of the CME as a macroscopic current. TcTc conductor insulator,anisotropicconductor

13. Where is it localized? Negative topological charge density Positive topological charge density

14. P.V. Buividovich, M.N. Chernodub, D.E. Kharzeev, T.K., E.V. Luschevskaya, M.I. Polikarpov (2010) Inverse Participation Ratio Inverse Participation Ratio (inverse volume of the distribution): Observables: Fractal dimension (performing the number of measurements with finite lattice spacing): „Chiral condensate“ for eigenvalue λ „Chirality“ = Topological charge density Unlocalized: ρ(x) = const,IPR = 1 Localized on a site: IPR = N Localized on fraction f of sites:IPR = 1/ f

15. P.V. Buividovich, M.N. Chernodub, D.E. Kharzeev, T.K., E.V. Luschevskaya, M.I. Polikarpov (2010) Localization of zero-modes Definition :

16. P.V. Buividovich, M.N. Chernodub, D.E. Kharzeev, T.K., E.V. Luschevskaya, M.I. Polikarpov (2010) Topological charge density Definition 1: Definition 2:

17. P.V. Buividovich, M.N. Chernodub, D.E. Kharzeev, T.K., E.V. Luschevskaya, M.I. Polikarpov (2010) Fractal dimension Our result: d = 2 ÷ 3 d = 0: instantons d = 1: percolating monopoles d = 2: percolating vortices d = 3: low-dim. domains About low-dimensional defects in QCD see also V.I. Zakharov, Phys.Atom.Nucl. 68 (2005) 573 [hep-ph/0410034]

18. Thank you for the attention! and Have a good time!