Chirality: from QCD to condensed matter

Transcription

1 High Energy Physics in the LHC Era, Valparaiso, Chile, 2012 Intersections between QCD and condensed matter, Schladming, Styria, Austria, March 1-6, 2015 Chirality: from QCD to condensed matter D. Kharzeev 1

2 Outline 1. Chirality, magnetic field, and chiral anomaly: an introduction 2. The Chiral Magnetic Effect 3. The Chiral Magneto-Hydrodynamics 4. Chirality and light

3 Systematics of anomalous conductivities Magnetic field Vorticity Vector current Axial current 3

4 G.Basar, DK, H.-U.Yee, PhysRevB89(2014) Anomalous transport and the Burgers equation Consider a hot Weyl semimetal with The chemical potential is then proportional to charge density: the CME current is and the charge conservation leads to

5 The Burgers equation Exactly soluble by Cole-Hopf transformation - initial value problem, integrable dynamics describes shock waves, solitons,...

6 Chirality and light

7 Chirality and light Photographs of a scarab beetle (Potosia aeruginosa jousselini) taken through a left- and a right-handed circular polarizer, showing that the cuticle reflects 7 left-handed circularly polarized light

8 Jet momentum, GeV The soft photon puzzle Every experiment that measured soft photons in processes with hadronic final states reported an anomalous enhancement. A recent and striking example: e + e - annihilation # of photons, 10-3 data: DELPHI Collaboration, 2010 Violation of the Low theorem?

9 Topology in (1+1) dimensions and jet fragmentation Massless (1+1) QED has many properties that resemble QCD: confinement, theta-vacuum, axial anomaly,... and is exactly soluble Use it to model the real-time dynamics of jet fragmentation! DK, F. Loshaj, arxiv: , , Phys Rev D Kinks of scalar field - quarks and antiquarks 9

10 Chiral magnetic wave in (1+1) as a source of photons data: DELPHI Collaboration, 2010 Solution of the soft photon puzzle? DK, F. Loshaj, Phys Rev D 89 (2014)7, Chiral anomaly induces coupled oscillations of chiral and electric charges; the latter radiate photons radiation off quark pairs produced from the vacuum

11 Plasmons in Dirac semimetals

12 Plasmons in Dirac semimetals The plasmon frequency is a dimensionful quantity; where does it originate from in a Dirac semimetal with chiral (massless) quasiparticles? Dimensional transmutation! DK, R. Pisarski, H.-U. Yee, arxiv:

13 Plasmons in Dirac semimetals DK, R. Pisarski, H.-U. Yee, arxiv: Expect universal properties of plasmons in all Dirac semimetals

14 THz radia)on (T- rays): the last fron)er in electromagne)c spectrum non-ionizing!

15 visible THz

16 Chirality and confinement?

17 The U A (1) problem in QCD QCD Lagrangian in the chiral limit of massless quarks possesses a global SU L (3)xSU R (3)xU A (1)xU V (1) symmetry; U A (1): When broken spontaneously, = 9 Goldstone bosons; experimentally, we observe only an octet the ninth would-be Goldstone η is very massive. This contradicts the Goldstone theorem! S.Weinberg, 75 17

18 The solution of the U A (1) problem Axial anomaly an explicit breaking of U A (1): brings in the topological Chern-Pontryagin density, implies connection to the periodic structure of the vacuum w.r.t. Chern-Simons coordinate 18

19 The theta-vacuum The instanton solutions in Minkowski space-time describe the tunneling events between the topological sectors of the vacuum marked by different integer values of N CS Z d 3 xk o Energy of gluon field N CS = instanton sphaleron 19

20 How penetrable are the barriers in the theta-vacuum? (how dilute is the instanton gas?) At small theta, write dilute instantons: Lattice: in the confined phase, instantons are not dilute C. Bonati et al, arxiv: Recent review: DK, arxiv:

21 The energy of electron in a crystal lattice ( empty lattice approximation, wikipedia) The energy of the QCD vacuum as a function of the theta angle E.Witten, PRL81(1998)2862 From: DK, R.Pisarski, M.Tytgat, arxiv:

22 Can this periodic structure of the vacuum be linked to confinement? DK and E.Levin, arxiv: The periodic structure of the vacuum is encoded in Veneziano s ghost saturating the Ward identity for the topological current: This procedure introduces the coupling of the ghost to the gluons: this coupling modifies the gluon propagator! 22

23 Analogy to Bloch crystal The tunneling of quasiparticles through the crystalline lattice leads to a similar ghost in the correlation function: D.Diakonov, M.Eides 81 Energy of gluon field even closer analogy if N CS = instanton sphaleron In perturbation theory, infinitely heavy electron! DK and E.Levin, arxiv:

24 Analogy to Bloch crystal In perturbation theory, infinitely heavy electron! in this limit, electrons in the crystal do not respond to photons. In QCD, this corresponds to the usual perturbation theory (the compact nature of SU(N) is ignored). However, at finite (non-zero susceptibility), the propagation of photons (gluons) is strongly affected by the crystalline lattice: 24

25 Topology as a cause of confinement? The Dyson-Schwinger equation for the gluon propagator: Solution: This is the Gribov propagator, proposed to solve the problem of gauge copies Complex poles at - confinement! Gluons cannot propagate at momenta smaller than DK and E.Levin, arxiv:

26 Glost n. Glost adj: Glosty Gluon dressed by ghost loops: the glost Glost is a multi-versatile word used to explain something positive or desirable, generally something that occurs between two close friends. Glost may also be used in place of other words, particularly the words that sound similar to Glost, such as "Lost" 26

27 How does the glost affect the running coupling of QCD? Since the topological susceptibility µ 4 exp( 1/g 2 ), using the glost in QCD amplitudes leads to expansion in powers of (g 2 ) n [exp( 1/g 2 )] m - trans-series? 27

28 The running QCD coupling DK and E.Levin, arxiv: Freezing (in YM) or vanishing (in QCD) in the IR running coupling cf dilute instantons: C.Callan, R.Dashen, D.Gross 78 L.Randall, R. Ratazzi, E.Shuryak 98 28

29 The glost and trans-series? Since the topological susceptibility µ 4 exp( 1/g 2 ), using the glost in QCD amplitudes leads to expansion in powers of (g 2 ) n [exp( 1/g 2 )] m - trans-series? 29

30 Outline Summary 1. Chirality, magnetic field, and chiral anomaly: an introduction 2. The Chiral Magnetic Effect 3. The Chiral Magneto-Hydrodynamics 4. Chirality and light