and anomaly-induced transport

Transcription

1 High Energy Physics in the LHC Era, Valparaiso, Chile, 2012 QCD in Strong Magnetic Fields, ECT*, Trento, November 12-16, 2012 The Chiral Magnetic Effect and anomaly-induced transport D. Kharzeev 1

2 Collaborators G. Basar (Stony Brook) Y. Burnier (Stony Brook -> Lausanne) G. Dunne (UConn) K. Fukushima (U Tokyo) J. Liao (BNL -> U. Indiana) L. McLerran (BNL) D. Son (U. Chicago) V. Skokov (BNL) H. Warringa (Frankfurt) H.-U. Yee (Stony Brook -> UIC) A. Zhitnitsky (U British Columbia) 2

3 Outline QCD in magnetic fields: why? Chiral Magnetic Effect: non-dissipative, topologically protected, quantum transport of charge Chiral magneto-hydrodynamics: how quantum anomalies affect the macroscopic collective behavior New results on CME from Quark Matter 2012 CME applications in real world

4 Why QCD in magnetic fields? Electromagnetic interactions (through DIS and e + e - annihilation) allowed to establish the existence of quarks and the QCD as the theory of strong interactions. Through the Bjorken scaling and deviations from it, the asymptotic freedom and the RG flow in QCD have been established.

5 Why QCD in magnetic fields? Later it has become clear that to understand QCD, we have to understand the properties of extended gluon field configurations, many of which have non-trivial topological contents. DIS is not an ideal tool to study these extended configurations - they yield power corrections that are difficult to decipher.

6 Why QCD in magnetic fields? To probe extended topological gluon field configurations, we need a different probe - an external, coherent electromagnetic field. Because of the existence of quark zero modes and associated topology, the magnetic field is ideal. However, usually the available magnetic field is weak, leading to small corrections; but, not so if - available in heavy ion collisions!

7 Gauge fields and topology NB: Maxwell electrodynamics as a curvature of a line bundle Möbius strip, the simplest nontrivial example of a fiber bundle Gauge theories live in a fiber bundle space that possesses non-trivial topology (knots, twists,...)

8 Atoms as knots in the ether P. Tait, Lord Kelvin (William Thomson) Knot theory (Tait, Alexander, Jones, Witten, Kontsevich, Khovanov,...)

9 Chern-Simons theory What does it mean for a gauge theory? Geometry Riemannian connection Curvature tensor Physics Gauge field Field strength tensor

10 Chern-Simons theory What does it mean for a gauge theory? Geometry Riemannian connection Physics Gauge field Curvature tensor S CS = k 8 M Field strength tensor d 3 x ijk A i F jk A i[a j,a k ] Abelian non-abelian

11 Chern-Simons theory S CS = k 8 M d 3 x ijk A i F jk A i[a j,a k ] Remarkable novel properties: gauge invariant, up to a boundary term topological - does not depend on the metric, knows only about the topology of space-time M breaks Parity invariance

12 Is there a way to observe topological charge fluctuations in experiment? + - excess of positive charge excess of negative charge Electric dipole moment of QCD matter! DK, Phys.Lett.B633(2006)260 [hep-ph/ ]

13 Is there a way to observe topological charge fluctuations in experiment? Relativistic ions create a strong magnetic field: H

14 Heavy ion collisions as a source of the strongest magnetic fields available in the Laboratory Talk by V.Skokov In a conducting plasma, Faraday induction can make the field long-lived: K.Tuchin, arxiv: DK, McLerran, Warringa, Nucl Phys A803(2008)227 46

15 Heavy ion collisions: the strongest magnetic field ever achieved in the laboratory 47

16 The Chern-Simons diffusion rate in an external magnetic field strongly coupled N=4 SYM plasma in an external U(1)R magnetic field through holography G. Basar, DK, arxiv: (PRD) weak field: strong field increases the rate: 15 dimensional reduction

17 Chiral Magnetic Effect in a chirally imbalanced plasma Chiral chemical potential is formally equivalent to a background chiral gauge field: In this background, and in the presence of B, vector e.m. current is not conserved: µ J µ = e2 F µ 16 F 2 L L,µ F µ R Compute the current through The result: J = e2 2 2 µ 5 Fukushima, DK, Warringa, PRD 08 F R,µ µ 5 = A 0 5 J µ = log Z[A µ,a 5 µ] A µ (x) e B J µ 5 Coefficient is fixed by the axial anomaly, no corrections 16

18 Chiral magnetic conductivity: discrete symmetries J = e2 2 2 µ 5 B P-odd T-odd P-odd P-odd effect! P-even T-odd T-even Non-dissipative current! (quantum computing etc) cf Ohmic conductivity: J = E P-even, T-odd, 17 dissipative

19 From QCD to electrodynamics: Maxwell-Chern-Simons theory L MCS = 1 4 F µ F µ A µ J µ + c 4 P µj µ CS. J µ CS = µ A F, Axial current of quarks Photons EM fields in QCD aether Annals Phys. 325 (2010)

20 The Chiral Magnetic Effect I: Charge separation B E = + cp B, =0 e eb 2 P d e = f q 2 f e eb S 2 L E =0 + e eb 2 =0 DK, Annals Phys. 325 (2010) e-print: arxiv:

21 Electric dipole moment of QCD instanton in an external magnetic field Quark zero mode density G. Basar, G. Dunne, DK, arxiv: [hep-th] Topological charge density Asymmetry between left and right modes induces the e.d.m. in an external B Talk by G.Dunne 20

22 Talk by P.Buividovich Numerical evidence for chiral magnetic effect in lattice gauge theory, P. Buividovich, M. Chernodub, E. Luschevskaya, M. Polikarpov, ArXiv ; PRD Red - positive charge Blue - negative charge SU(2) quenched, Q = 3; Electric charge density (H) - Electric charge density (H=0)

23 Talk by P.Buividovich Numerical evidence for chiral magnetic effect in lattice gauge theory, P. Buividovich, M. Chernodub, E. Luschevskaya, M. Polikarpov, ArXiv ; PRD Red - positive charge Blue - negative charge SU(2) quenched, Q = 3; Electric charge density (H) - Electric charge density (H=0)

24 Chiral magnetic effect in 2+1 flavor QCD+QED, M. Abramczyk, T. Blum, G. Petropoulos, R. Zhou, ArXiv ; Red - positive charge Blue - negative charge 2+1 flavor Domain Wall Fermions, fixed topological sectors, 16^3 x 8 lattice

25 No sign problem for the chiral chemical potential - direct lattice studies are possible Fukushima, DK, Warringa, PRD 08 23

26 Talk by A. Yamamoto arxiv: , PRL 24

27 Talk by K.Landsteiner Holographic chiral magnetic effect: the strong coupling regime (AdS/CFT) he induced j = B,. For con Strong coupling ( ) Weak coupling 0 H.-U. Yee, arxiv: , JHEP 0911:085, 2009; V. Rubakov, arxiv: ,... A. Rebhan, A.Schmitt, S.Stricker JHEP 0905, 084 (2009), G.Lifshytz, M.Lippert, arxiv: ;.A. Gorsky, P. Kopnin, A. Zayakin, arxiv: , CME persists at strong coupling - hydrodynamical formulation? 0 10 /T D.K., H. Warringa Phys Rev D80 (2009)

28 Hydrodynamics: an effective low-energy Theory Of Everything (TOE) Hydrodynamics states that the response of the fluid to slowly varying perturbations is completely determined by conservation laws (energy, momentum, charge,...) Little Bang Big Bang 26

29 The remarkable success of hydrodynamics at RHIC and LHC R. Snellings [ALICE Coll.] Talk at QM

30 Quantifying the transport properties of QCD matter Hydrodynamics: an effective low-energy theory, expansion in the ratio of thermal length 1/T to the typical variation scale L, Each term in this derivative expansion is multiplied by an appropriate transport coefficient very small shear viscosity - perfect liquid ; strong coupling 1 LT 28

31 Talk by V.Zakharov Hydrodynamics and anomalies Hydrodynamics: an effective low-energy TOE. States that the response of the fluid to slowly varying perturbations is completely determined by conservation laws (energy, momentum, charge,...) Conservation laws are a consequence of symmetries of the underlying theory What happens to hydrodynamics when these symmetries are broken by quantum effects (anomalies of QCD and QED)? 29

32 Chiral MagnetoHydroDynamics (CMHD) - relativistic hydrodynamics with triangle anomalies and external electromagnetic fields First order (in the derivative expansion) formulation: D. Son and P. Surowka, arxiv: Constraining the new anomalous transport coefficients: positivity of the entropy production rate, µs µ 0 CME (for chirally imbalanced matter) 30

33 Chiral MagnetoHydroDynamics (CMHD) - relativistic hydrodynamics with triangle anomalies and external electromagnetic fields First order hydrodynamics has problems with causality and is numerically unstable, so second order formulation is necessary; Complete second order formulation of CMHD with anomaly: DK and H.-U. Yee, ; Phys Rev D Many new transport coefficients - use conformal/weyl invariance; still 18 independent transport coefficients related to the anomaly. 15 that are specific to 2nd order: new Many new anomaly-induced phenomena! 31

34 Chiral MagnetoHydroDynamics (CMHD) - relativistic hydrodynamics with triangle anomalies and external electromagnetic fields Positivity of entropy production - still too many unconstrained transport coefficients... DK and H.-U. Yee, Is there another guiding principle? 32

35 No entropy production from T-even anomalous terms J = e2 2 2 µ 5 B DK and H.-U. Yee, P-odd T-odd P-even T-odd P-odd cf Ohmic P-odd effect! conductivity: J = E T-odd, T-even dissipative Non-dissipative current! 33 (time-reversible - no arrow of time, no entropy production)

36 No entropy production from P-odd anomalous terms DK and H.-U. Yee, Entropy grows µs µ 0 Mirror reflection: entropy decreases? µs µ 0 Decrease is ruled out by 2nd law of thermodynamics µs µ =0 34

37 No entropy production from T-even anomalous terms 1st order hydro: Son-Surowka results are reproduced 2nd order hydro: 13 out of 18 transport coefficients are computed; but is the guiding principle correct? DK and H.-U. Yee, Can we check the resulting relations between the transport coefficients? e.g. 35

38 The fluid/gravity correspondence Long history: Hawking, Bekenstein, Unruh; Damour 78; Thorne, Price, MacDonald 86 (membrane paradigm) Recent developments motivated by AdS/CFT: Policastro, Kovtun, Son, Starinets 01 (quantum bound) Bhattacharya, Hubeny, Minwalla, Rangamani 08 (fluid/gravity correspondence) Some of the transport coefficients of 2nd order hydro computed; enough to check some of our relations, e.g. J. Erdmenger et al, ; N. Banerjee et al, It works Other holographic checks work as well: 36 DK and H.-U. Yee,

39 The chiral magnetic current is non-dissipative: protected from (local) scattering and dissipation by (global) topology Somewhat similar to superconductivity, but exists at any temperature! (?) Anomalous transport coefficients in hydrodynamics describe dissipation-free processes (unlike e.g. shear viscosity) 37

40 The CME in relativistic hydrodynamics: The Chiral Magnetic Wave DK, H.-U. Yee, arxiv: [hep-th]; PRD CME Chiral separation Chiral Propagating chiral wave: (if chiral symmetry is restored) Electric Gapless collective mode is the carrier of CME current in MHD: 38

41 The Chiral Magnetic Wave The velocity of CMW computed in Sakai-Sugimoto model (holographic QCD) In strong magnetic field, CMW propagates with the speed of light! Chiral Electric DK, H.-U. Yee, arxiv: [hep-th], PRD 39

42 Charge asymmetry w.r.t. reaction plane as a signature of strong P-odd fluctuations + - excess of positive charge excess of negative charge Electric dipole moment of QCD matter! DK, Phys.Lett.B633(2006)260 [hep-ph/ ]

43 Slide from S. Voloshin

44 NB: P-even quantity (strength of P-odd fluctuations)

45 S.Esumi et al [PHENIX Coll] April 2010

46 Phenomenological estimates DK, L.McLerran, H.Warringa, arxiv: (Real-time) lattice value for the sphaleron rate, estimate for magnetic field and its lifetime yield a rough (by the order of magnitude) agreement with the data, but uncertainties are large 44

47 Talk by B.Muller Are the observed fluctuations of charge asymmetries a convincing evidence for the CME? A number of open questions that still have to be clarified: in-plane vs out-of-plane, new observables? arxiv: ; ;... e.g. A. Bzdak, V. Koch, J. Liao, estimates of the asymmetries e.g. M. Asakawa, A. Majumder, B. Muller, arxiv: backgrounds e.g. S. Pratt and S. Schlichting, arxiv: F. Wang, arxiv: ;... Fortunately, a number of new analytical and lattice results (many reported here), and the new data (low energy, U-U, charge-asymmetry driven flow) 45 has become available! (much of it at Quark Matter 2012)

48 News from Quark Matter

49 G. Wang et al [STAR Coll], arxiv: [nucl-ex] Disappearance of charge separation in the beam energy scan at RHIC Signal disappears 47

50 G. Wang et al [STAR Coll], arxiv: [nucl-ex] CME vs background effects: a test using the UU collisions S. Voloshin, arxiv: (PRL) All backgrounds to CME are driven by the elliptic flow (e.g. v2 + charge balance functions, etc) The idea: U is a highly deformed nucleus; because of this, even in the absence of spectators and thus in the absence of magnetic field, the elliptic flow does not vanish. If the charge separation persists, it is driven by background; if it vanishes, it is driven by magnetic field 48 (CME)

51 G. Wang et al [STAR Coll], arxiv: [nucl-ex] CME vs background effects: a test using the UU collisions The effects of deformation are clearly seen in UU collisions: broader multiplicity distribution, larger elliptic flow 49

52 G. Wang et al [STAR Coll], arxiv: [nucl-ex] CME vs background effects: a test using the UU collisions Signal disappears at non-zero v2 - support for CME interpretation 50

53 G. Wang et al [STAR Coll], arxiv: [nucl-ex] 51

54 CME studies at the LHC ALICE Coll., arxiv:

55 CME studies at the LHC: higher harmonics ALICE Coll., arxiv:

56 Testing the Chiral Magnetic Wave at RHIC Finite baryon density + CMW = electric quadrupole moment of QGP. Signature - difference of elliptic flows of positive and negative pions determined by total charge asymmetry of the event A: at A>0, v2(-) > v2(+); at A<0, v2(+) > v2(-) Y.Burnier, DK, J.Liao, H.Yee, PRL

57 G. Wang et al [STAR Coll], arxiv: [nucl-ex] Testing the CMW at RHIC 55

58 G. Wang et al [STAR Coll], arxiv: [nucl-ex] Testing the CMW at RHIC 56

59 A new test: baryon asymmetry DK, D.T.Son arxiv: ; PRL CME Vorticity-induced Chiral Vortical Effect CME: (almost) only electric charge CVE: (almost) only baryon charge There has to be a positive correlation between 57 electric charge and baryon number! mixed correlators - e.g. +

60 Another effect related to anomalies and magnetic fields: Conformal anomaly as a source of soft photons and dileptons in heavy ion collisions Talk by V. Skokov G.Basar, DK, V.Skokov, PRL 12 58

61 Chiral fermions and topology in condensed matter systems Novel appplications: graphene, TIs, Weyl semimetals Massless (2+1) fermions M.Muller, J.Schmalian, L. Fritz, Similar to QGP in several ways: strongly coupled, perfect liquid behavior, chiral fermions,.. Magnetized graphene: e.g. I.Aleiner, DK, A. Tsvelik, Phys Rev B 07; M.Khodas, I.Zaliznyak, DK, Phys Rev B 09

62 Chiral electronics Weyl semimetal quantum amplifier - sensor of ultra-weak magnetic field DK, H.-U.Yee, arxiv:

63 Summary Interplay of topology, anomalies and magnetic field leads to the Chiral Magnetic Effect; confirmed by lattice QCD x QED, mounting evidence from RHIC and LHC CME and related anomaly-induced phenomena are an integral part of relativistic hydrodynamics (Chiral MagnetoHydroDynamics) Many open theoretical problems, important new applications also outside of nuclear science (spintronics, quantum computing,energy storage,...)