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Anomalous parity violation, chiral magnetic effect and holography Ingo Kirsch

`. T. Kalaydzhyan and I.K., PRL 106 (2011) 211601 arXiv:1102.4334 [hep-th]. Anomalous parity violation, chiral magnetic effect and holography Ingo Kirsch DESY Hamburg, Germany. DESY Theory Workshop 2011 Cosmology meets Particle Physics: Ideas & Measurements.

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Anomalous parity violation, chiral magnetic effect and holography Ingo Kirsch

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  1. ` T. Kalaydzhyan and I.K., PRL 106 (2011) 211601 arXiv:1102.4334 [hep-th] Anomalous parity violation, chiral magnetic effect and holography Ingo Kirsch DESY Hamburg, Germany DESY Theory Workshop 2011 Cosmology meets Particle Physics: Ideas & Measurements

  2. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch 2 Overview • I. Anomalous P- and CP- violation & chiral magnetic effect • - Motivation: charge asymmetry in heavy-ion collisions (HIC) • - Phenomenology of the Chiral Magnetic Effect (CME) • - Motivation for cosmologists: Strong Matter vs. Matter in the Early Universe • II. CME in hydrodynamics • - N-charge model (Son & Surowka) • - reduction to two charges yields CME and similar effects • Fluid/gravity model of the CME • - three-charge STU model plus background gauge fields • - reduction to two charges yields holographic CME • Conclusions • - Does the CME explain the observed charge asymmetry? • - Summary and critical remarks ETH Zurich, 30 June 2010

  3. Holography of non-equilibrium plasmas DESY Theory Workshop 2011 -- Ingo Kirsch 3 Part I: Anomalous P- and CP- violation & chiral magnetic effect 4 University of Chicago, 23 April 2007

  4. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch 4 Motivation: Observed charge asymmetry in HICs Heavy-ion collision: Excess of positive charge (above YR) + - Excess of negative charge (below YR)

  5. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch 5 Motivation: Observed charge asymmetry in HICs Azimuthal two-particle correlation with respect to the reaction plane: (=measure for the charge asymmetry) STAR collaboration data (RHIC): Observation: - separation of negatively and positively charged particles along the system’s angular momentum - seen in same-charge correlations - larger correlation for more peripheral collisions (Possible) theoretical explanation: chiral magnetic effect STAR Coll., PRL 103 (’09) 251601, STAR Coll., PRC 81 (’10) 054908 + -

  6. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch 6 Heavy-ion collisions and magnetic field Au-Au collisions at Brookhaven’s RHIC and (since Nov. 2010) Pb-Pb collisions at LHC form a thermal plasma of quarks and gluons: Strong magnetic fields expected at early stages of the collision: quarks will be polarized in the direction perpendicular to reaction plane (UrQMD) time scale: 10-24 s length scale: 10-15 m before the collision quark-gluon-plasma hadronization Kharzeev, McLerran, Warringa (2008) ETH Zurich, 30 June 2010

  7. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch 7 Topological configurations with nonzero winding number Transitions between Yang-Mills vacua: n = winding number = topological invariant Instanton: configuration interpreted as a tunneling effect between two different vacua, exponentially suppressed at finite temperature Sphaleron: configuration which jumps over the barrier, not suppressed at finite temperature, production rate topological charge fluctuations expected in quark gluon plasma ETH Zurich, 30 June 2010

  8. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch 8 Topological charge fluctuations gluon configurations have topological charge: avarage (over many events): but there are fluctuations: ! event-by-event or local P- and CP-violation lattice simulation: red: positive topological charge density blue: negative topological charge density Two different gluon configurations (picture courtesy: T. Kalaydzhyan)

  9. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch 9 Topological charge fluctuations change chirality of quarks Axial anomaly: axial current not conserved in QCD Adler (1969), Bell and Jackiw (1969) integrate over space and time: NL,R = number of quarks (& antiquarks) with left- and right-handed helicity topological charge induces chirality, i.e. an asymmetry between the number of left- and . right-handed quarks (number of left- and right-handed quarks differs in each event) introduce chiral chemical potential Nonperturbative (event-by-event) P- and CP-violating effect

  10. Anomalous parity violation, chiral magn. effect and holography + - DESY Theory Workshop 2011 -- Ingo Kirsch Chiral magnetic effect Charge separation in QGP: Kharzeev, McLerran & Warringa (2008) 1. in presence of a magnetic field B, momenta of the quarks align along B 2. topological charge induces chirality (e.g. Q = −1 converts a left-handed quark into a right-handed quark) 3. positively/negatively charged quarks move up/down (charge separation!) 4. an electric current is induced along the magnetic field B Chiral Magnetic Effect (C=anomaly coefficient) sphaleron background spin mom. 10

  11. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch Chiral magnetic effect on the lattice (numerical results) Braguta, Buividovich, Kalaydzhyan, Kuznetsov, Polikarpov (2010) . The fluctuations of the el.-magn. current increase with . 11 ETH Zurich, 30 June 2010

  12. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch Strong vs. Early Universe Matter (baryogenesis) Matter produced in heavy-ion collisions Matter produced in the early universe (ALICE CERN) Topological charge changing transitions chiral asymmetry: 1. induce difference in the number of left- and right-handed quarks 2. P and CP violation (local) 3. out-of-equilibrium Observation: Does this explain the observed charge asymmetry in HICs? Sakharov conditions (baryon no. asym.): 1. induce baryon&lepton number violation Kuzmin, Rubakov, Shaposhnikov (1985) 2. C and CP violation 3. out-of-equilibrium Observation: asymmetry between matter and anti-matter 12 ETH Zurich, 30 June 2010

  13. Holography of non-equilibrium plasmas DESY Theory Workshop 2011 -- Ingo Kirsch Part II: CME in hydrodynamics 13 4 University of Chicago, 23 April 2007

  14. Anomalous parity violation, chiral magn. effect and holography 14 DESY Theory Workshop 2011 -- Ingo Kirsch Hydrodynamical model with N anomalous U(1) charges Son & Surowka (2009) U(1)N plasma with triangle anomalies: stress-energy tensor Tmnand U(1) currents jam : E- & B-fields, vorticity: “New” transport coefficients (not listed in Landau-Lifshitz) - vortical conductivities Erdmenger, Haack, Kaminski, Yarom (2008) - magnetic conductivities Son & Surowka (2009) first found in a holographic context (AdS/CFT) ETH Zurich, 30 June 2010

  15. Anomalous parity violation, chiral magn. effect and holography 15 DESY Theory Workshop 2011 -- Ingo Kirsch First-order transport coefficients Son & Surowka (2009), Neiman & Oz (2010) U(1) currents: vortical and magn. conductivities: Conductivities are non-zero only in fluids with triangle anomalies! comments: - first term is the complete response to the external magnetic field - second term is frame dependent (here Landau frame) and subtracts the contribution to the current due to the drag of the fluid Amado, Landsteiner, Pena-Benitez (2011) chemical potentials coffee with sugar (chiral molecules) ETH Zurich, 30 June 2010

  16. Anomalous parity violation, chiral magn. effect and holography 16 DESY Theory Workshop 2011 -- Ingo Kirsch Two charge case: U(1)A x U(1)V Kalaydzhyan & I.K. (2011) Hydrodynamical equations: Identifications: axial gauge field switched off! Constitutive equations: ETH Zurich, 30 June 2010

  17. Anomalous parity violation, chiral magn. effect and holography 17 DESY Theory Workshop 2011 -- Ingo Kirsch (Chiral) magnetic and vortical effects constitutive equations: transport coefficients (conductivities): C=chiral since CVE, CME prop. to chiral chemical potential m5 Q=quark since QVE, QME prop. to quark chemical potential m (QME also called chiral separation effect (CSE)) creates an effective magnetic field Kharzeev and Son (2010) Effects agree to leading order with Sadofyev and Isachenkov (2010) CVE QVE CME QME ETH Zurich, 30 June 2010

  18. Holography of non-equilibrium plasmas DESY Theory Workshop 2011 -- Ingo Kirsch Part III: Fluid/gravity model of the CME Kalaydzhyan & I.K., PRL 106 (2011) 211601 18 4 University of Chicago, 23 April 2007

  19. Anomalous parity violation, chiral magn. effect and holography 19 DESY Theory Workshop 2011 -- Ingo Kirsch Hydrodynamics vs. fluid/gravity model Hydrodynamics Fluid/gravity model Multiple-charge model Holographic three-charge model U(1)Nplasma with triangle anomalies STU model with ext. background fields Son & Surowka (2009)(AdS black hole with three U(1)’s) Two-charge model Holographic two-charge model U(1)V x U(1)A plasma STU model reduced to two charges recover CME (and other effects) recover holographic CME, etc. dual N=3 reduction ETH Zurich, 30 June 2010

  20. Anomalous parity violation, chiral magn. effect and holography 20 DESY Theory Workshop 2011 -- Ingo Kirsch Gravity: Holographic computation (strategy) Kalaydzhyan & I.K. PRL 106 (2011) 211601 Strategy: - quark-gluon plasma is strongly-coupled use AdS/CFT to compute the transport coefficients relevant for the anomalous effects (CME, etc.) - find a 5d charged AdS black hole solution with several U(1) charges (the 4d fluid (QGP) lives on the boundary of that space) - use fluid-gravity methods to holographically compute the transport coefficients - recover chiral magnetic effect, etc. Hawking temperature is temperature of the fluid ETH Zurich, 30 June 2010

  21. Anomalous parity violation, chiral magn. effect and holography 21 DESY Theory Workshop 2011 -- Ingo Kirsch Gravity: Three-charge STU model A prototype of an AdS black hole solution with three U(1) charges is the socalled STU solution (known from string theory) Behrndt, Cvetic, Sabra (1999) D=5, N=2 gauged supergravity Lagrangian: Fields: - metric gMN , where M, N = 0, ..., 4. - three U(1) gauge fields AMa , where a = 1, 2, 3. - three real scalars Xa - metric on scalar manifold: The information of the anomalies is encoded in the Chern-Simons coefficients ETH Zurich, 30 June 2010

  22. Anomalous parity violation, chiral magn. effect and holography background gauge field added (needed to model ext. B-field)! 22 DESY Theory Workshop 2011 -- Ingo Kirsch Boosted STU solution 5d R-charged black hole solution: with three charges qa ETH Zurich, 30 June 2010

  23. Anomalous parity violation, chiral magn. effect and holography 23 DESY Theory Workshop 2011 -- Ingo Kirsch First-order transport coefficients We use the standard procedure of Bhattacharyya et al. (2008) to holographically compute the transport coefficients (Torabian & Yee (2009))and : - vary 4-velocity and background fields (up to first order): - The boosted black-brane solution (0th order sol.) is no longer an exact solution, but receives higher-order corrections. - solve equations of motion for this case and find corrections to the metric, gauge fields and scalars - read off corrections from the near-boundary expansion (Fefferman-Graham coordinates): ETH Zurich, 30 June 2010

  24. Anomalous parity violation, chiral magn. effect and holography 24 DESY Theory Workshop 2011 -- Ingo Kirsch First-order transport coefficients (cont.) • - cf. w/ • - zeroth order: • - first order: We recover the hydrodynamic result! ETH Zurich, 30 June 2010

  25. Anomalous parity violation, chiral magn. effect and holography 25 DESY Theory Workshop 2011 -- Ingo Kirsch Holographic magnetic and vortical effects Using the same identifications as in hydrodynamics, but now for the holographically computed transport coefficients, we get Result: CME, CVE, etc. are realized in the STU-model (plus background gauge field), when appropriately reduced to a two-charge model. CVE QVE CME QME ETH Zurich, 30 June 2010

  26. Holography of non-equilibrium plasmas DESY Theory Workshop 2011 -- Ingo Kirsch Part IV: Discussion and Conclusions 26 4 University of Chicago, 23 April 2007

  27. Anomalous parity violation, chiral magn. effect and holography 27 DESY Theory Workshop 2011 -- Ingo Kirsch Does the CME explain the observed charge asymmetry? • Some problems: • anisotropy (v2) dependence • Charge Separation Out-of-plane or In-plane? • observation seems to suggest in-plane • Magnitude of the charge separation generated by the CME might not be large enough to explain the signal observed in the STAR experiment. • B. Müller, A. Schäfer, Phys. Rev. C82 (’10) 057902 Charge asymmetry as a function of the event-by-event anisotropy (v2obs) of the measured particles in the 20–40% centrality (B=const.) observation: asymmetry is proportional to v2 (interpretation is still under investigation) CME: does not depend on v2 picture courtesy: Quan Wang, Purdue Univ. ETH Zurich, 30 June 2010

  28. Anomalous parity violation, chiral magn. effect and holography 28 DESY Theory Workshop 2011 -- Ingo Kirsch Conclusions • Chiral magnetic effect: Generation of an electric current in topological non-trivial • backgrounds in the presence of a magnetic field B (local parity violating effect). Expected to • appear in the quark-gluon-plasma generated in heavy-ion collisons. • I described how the effect appears in hydrodynamics and presented a holographic (AdS/CFT) computation of the relevant transport coefficients (using fluid-gravity duality of an AdS-Reissner-Nordstrom-like solution with two U(1) charges). • Does the CME explain the charge asymmetry observed in heavy-ion collisions? • If yes, the local parity violation would constitute the first direct observation of a • topological effect in non-Abelian gauge theories. • This is heavily investigated both theoretically and experimentally (RHIC & LHC) at the moment. There is no final answer, yet.

  29. Anomalous parity violation, chiral magn. effect and holography 29 DESY Theory Workshop 2011 -- Ingo Kirsch Thank you! ETH Zurich, 30 June 2010

  30. Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop 2011 -- Ingo Kirsch A Chiral magnetic effect in quark-gluon plasma Heavy-ion collision: Excess of positive charge (above YR) + - Excess of negative charge (below YR)

  31. Anomalous parity violation, chiral magn. effect and holography B DESY Theory Workshop 2011 -- Ingo Kirsch Comments i) second order effects: The effects of the chiral anomaly on the axial charge density appear at second order. This is an advantage over AdS/QCD models of the chiral magnetic effect. Fluid/gravity duality captures (small) deviations from equilibrium. Summary: CME, etc. are first-order effects in the currents, while the change of the axial charge density due to the anomaly is a second-order effect. ii) caveats: - unlike in string theory we keep unfixed - we prescind from the strict string interpretation of the three U(1)’s as R-charges STU model becomes a phenomenological model ETH Zurich, 30 June 2010

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