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

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 III.Fluid/gravity model of the CME - three-charge STU model plus background gauge fields - reduction to two charges yields holographic CME IV.Conclusions - Does the CME explain the observed charge asymmetry? - Summary and critical remarks Overview ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography 2 DESY Theory Workshop Ingo Kirsch

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

4 Anomalous parity violation, chiral magn. effect and holography Motivation: Observed charge asymmetry in HICs Heavy-ion collision: Excess of positive charge (above Y R ) Excess of negative charge (below Y R ) + -

5 DESY Theory Workshop Ingo Kirsch Anomalous parity violation, chiral magn. effect and holography 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) , STAR Coll., PRC 81 (’10)

Heavy-ion collisions and magnetic field ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography 6 DESY Theory Workshop Ingo Kirsch 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 before the collision quark-gluon-plasma hadronization (UrQMD) time scale: s length scale: m Kharzeev, McLerran, Warringa (2008)

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 Topological configurations with nonzero winding number ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography 7 DESY Theory Workshop Ingo Kirsch

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) 8 DESY Theory Workshop Ingo Kirsch Anomalous parity violation, chiral magn. effect and holography Topological charge fluctuations

9 DESY Theory Workshop Ingo Kirsch Anomalous parity violation, chiral magn. effect and holography 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: N L,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

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) DESY Theory Workshop Ingo Kirsch Anomalous parity violation, chiral magn. effect and holography Chiral magnetic effect spin mom. + - sphaleron background 10

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

Topological charge changing transitions Matter produced in heavy-ion collisions Strong vs. Early Universe Matter (baryogenesis) ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography DESY Theory Workshop Ingo Kirsch (ALICE CERN) Matter produced in the early universe 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

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

U(1) N plasma with triangle anomalies: stress-energy tensor T mn and U(1) currents j am : Hydrodynamical model with N anomalous U(1) charges ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography “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) E- & B-fields, vorticity: Son & Surowka (2009) 14 DESY Theory Workshop Ingo Kirsch

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) First-order transport coefficients ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography chemical potentials Son & Surowka (2009), Neiman & Oz (2010) 15 DESY Theory Workshop Ingo Kirsch coffee with sugar (chiral molecules)

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

(Chiral) magnetic and vortical effects ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography constitutive equations: transport coefficients (conductivities): C=chiral since CVE, CME prop. to chiral chemical potential m 5 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) CME QME CVE QVE 17 DESY Theory Workshop Ingo Kirsch

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

Hydrodynamics vs. fluid/gravity model ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography reduction dual N=3 19 DESY Theory Workshop Ingo Kirsch Hydrodynamics Fluid/gravity model Multiple-charge model Holographic three-charge model U(1) N plasma 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.

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 Gravity: Holographic computation (strategy) ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography 20 DESY Theory Workshop Ingo Kirsch Kalaydzhyan & I.K. PRL 106 (2011)

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 g MN, where M, N = 0,..., 4. - three U(1) gauge fields A M a, where a = 1, 2, 3. - three real scalars X a - metric on scalar manifold: Gravity: Three-charge STU model ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography 21 DESY Theory Workshop Ingo Kirsch The information of the anomalies is encoded in the Chern-Simons coefficients

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

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 (0 th 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): First-order transport coefficients ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography 23 DESY Theory Workshop Ingo Kirsch

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

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. Holographic magnetic and vortical effects ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography CME QME CVE QVE 25 DESY Theory Workshop Ingo Kirsch

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

Some problems: anisotropy (v 2 ) 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) Charge asymmetry as a function of the event-by-event anisotropy (v 2 obs ) of the measured particles in the 20–40% centrality (B=const.) observation: asymmetry is proportional to v 2 (interpretation is still under investigation) CME: does not depend on v 2 Does the CME explain the observed charge asymmetry? ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography 27 DESY Theory Workshop Ingo Kirsch picture courtesy: Quan Wang, Purdue Univ.

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. Conclusions Anomalous parity violation, chiral magn. effect and holography 28 DESY Theory Workshop Ingo Kirsch

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

A Anomalous parity violation, chiral magn. effect and holography Chiral magnetic effect in quark-gluon plasma Heavy-ion collision: Excess of positive charge (above Y R ) Excess of negative charge (below Y R ) + -

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 Comments ETH Zurich, 30 June 2010 Anomalous parity violation, chiral magn. effect and holography B DESY Theory Workshop Ingo Kirsch