INT, Seattle, March 18, 2021 Chiral Magnetic Effect: from quarks to quantum computers Dmitri Kharzeev 1 Outline 1. What is Chirality? 2. Chirality and transport 3. Chiral Magnetic Effect (CME): chiral transport induced by quantum anomaly 4. CME as a probe of gauge field topology 5. CME in heavy ion collisions and the RHIC isobar run 6. Broader implications: a) Dirac and Weyl materials b) quantum computing with CME Disclaimer: not a systematic review of ongoing developments 3 min introduction to CME on : https://www.youtube.com/watch?v=n4L7VPpEwqo&ab_channel=MeisenWang Chirality: the definition Greek word: χειρ (cheir) - hand Lord Kelvin (1893): “I call any geometrical figure, or groups of points, chiral, and say it has chirality, if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself.” Test of chirality: mirror reflection Parity transformation: mirror reflection + 1800 rotation 5 Chirality: DNA Chirality: DNA De Witt Sumners, Notices of the AMS, 1995 Living organisms contain almost only left-handed (LH) amino-acids and right-handed (RH) sugars – you would starve on LH sugar! (artificial sweeteners) 2500 chiral drugs! (most of the new) www.rowland.harvard.edu/rjf/fischer Thalidomide 1962: FDA pharmacologist W. White, “Breaking Bad”, Season 1, episode 2 Frances Oldham Kelsey receives the President's Award for Left-handed molecule is a drug; Distinguished Federal right-handed is a poison: Civilian Service from President John F. birth defects, 50% death rate. Kennedy for blocking sale of thalidomide in Synthetic: equal mixture the United States. Methamphetamine Levmethamphetamine 50 mg Chiral transport, 240 B.C. The Archimedes screw 11 Parity transformation: mirror reflection + 1800 rotation Leonardo da Vinci 1452-1519 12 Chiral propulsion ? vector pseudo-vector Velocity parallel to angular velocity requires the breaking of parity: chiral propeller Chiral propulsion T-odd T-odd T-even E.Purcell ’76 Chiral propulsion in the Stokes regime A.Shapere, F.Wilczek ‘88 is non-dissipative (T-even) and determined entirely by geometry; it does not depend on viscosity! S.Ayf, I.Kuk, DK, arXiv:1804.08664 Classical analog of anomaly-induced transport that we are now going to consider Chirality and quantum transport Chiral fermions Majorana fermions: 1937 Dirac equation: Weyl fermions: E.Majorana, 1906-38? P. Dirac, 1928 H. Weyl, 1929 Fermions: E. Fermi,1925 Currents in a magnetic field ? vector pseudo-vector An electric current parallel to B requires a parity breaking Currents in a magnetic field Consider a gas of massless charged Weyl fermions of a certain chirality, say left-handed (cf weak interactions) Put this gas in an external magnetic field B; the interaction of spin with B, and the locking of momentum to spin induce the current But: no current in equilibrium Bloch theorem, … C.N. Yang Early work on currents in magnetic field due to P violation (see DK, Prog.Part.Nucl.Phys. 75 (2014) 133 for a complete (?) list of references) A.Vilenkin (1980) “Equilibrium parity-violating current in a magnetic field”; (1980) “Cancellation of equilibrium parity-violating currents” G. Eliashberg (1983) JETP 38, 188 L. Levitov, Yu.Nazarov, G. Eliashberg (1985) JETP 88, 229 M. Joyce and M. Shaposhnikov (1997) PRL 79, 1193; M. Giovannini and M. Shaposhnikov (1998) PRL 80, 22 A. Alekseev, V. Cheianov, J. Frohlich (1998) PRL 81, 3503 20 The way out: chiral anomaly For massless fermions, the axial current is conserved classically due to the global UA(1) symmetry: However this conservation law is destroyed by quantum effects S. Adler ‘69 J. Bell, R. Jackiw ’69 The chiral charge is not conserved; a chirally imbalanced state of chiral fermions is not a true ground state of the system! Dirac sea Left Right Dirac sea as Hilbert’s infinite hotel Left Right Image credit: OSA Chiral anomaly LEFT RIGHT E E In classical background fields (E and B), chiral Chiral anomaly anomaly induces an k imbalance between left- ​|$⟩ and right-handed ​|"⟩ fermions; chiral chemical potential: Adler; Bell, Jackiw (1969); Nielsen, Ninomiya (1983) 24 Chirality in 3D: the Chiral Magnetic Effect chirality + magnetic field = current spin momentum 25 DK, L.McLerran, H. Warringa ‘07 Chiral Magnetic Effect DK’04; DK, A. Zhitnitsky ‘07; DK, L.McLerran, H.Warringa ’07; K.Fukushima, DK, H.Warringa, “Chiral magnetic effect” PRD’08; Review and list of refs: DK, arXiv:1312.3348 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 generated: Compute the current through Absent in Maxwell theory! Coefficient is fixed by the chiral anomaly, no corrections 26 Chirally imbalanced system is a non-equilibrium, steady state Chiral Magnetic Effect Alternative derivation: K.Fukushima, DK, H.Warringa, “Chiral magnetic effect” PRD’08; Consider the thermodynamical potential at finite : Compute the current through using 27 Chiral magnetic conductivity: discrete symmetries P – parity T – time reversal P-odd P-even T-odd T-odd P-odd cf Ohmic P-odd effect! conductivity: Effect persists in hydrodynamics! T-odd, T-even dissipative Non-dissipative current! 28 (topologically protected) Systematics of anomalous conductivities Magnetic field Vorticity Vector current Axial current 29 Systematics of anomalous conductivities Magnetic field Vorticity Vector current Axial current Breaking of equivalence principle at finite T? 30 M.Buzzegoli, DK, arXiv:2102.01676 Understanding Chern-Simons current Consider electromagnetic wave with frequency ω; the electric field fluctuates: in Coulomb gauge , away from source: (“radiation gauge”) the time-averaged Chern-Simons current becomes: For circularly polarized light moving along z axis: Chiral anomaly – transfer of chirality from light to fermions photon number of photons helicity S.Kaushik, DK, E.Philip, PRB 99(2019)075150 Chern-Simons number Consider now the CS density: the integral of this quantity is known as magnetic helicity: [Abelian part of CS 3-form] What is the physical meaning? again, let us use the Coulomb gauge: magnetic helicity then takes the form: that can be considered as a sum over the Gauss linking numbers of magnetic flux: Moffatt 1969, Arnold, Khesin 1998 Berger 1999 Chern-Simons number: magnetic helicity Anomaly implies non-conservation of CS number in Coulomb gauge, flux of circularly polarized photons through the surface Reconnection of magnetic flux (change of magnetic helicity) induces an electric field – can there be an electric current? Chern-Simons number: magnetic helicity Magnetic helicity: Non-Abelian CS: Jones polynomials, … Witten ‘89 self-linking Gauss linking Change of magnetic helicity is due to ”magnetic reconnections”: Y.Hirono, DK, Y.Yin PRL117(2016)172301 Magnetic helicity and CME Y.Hirono, DK, Y.Yin PRL117(2016)172301 If chiral fermions are present, the induced electric field will change the fermi-momentum differently for R and chiralities: Density of states of R antiparticles: and L particles: CME from the change of topology Y.Hirono, DK, Y.Yin PRL117(2016)172301 In (1+1) dimensions, chirality = direction of motion, so R and L fermions move in opposite directions, and carry currents: antiparticle; moves to the right (+ direction) moves to the left (+ direction); particle Magnetic helicity and CME Magnetic helicity: self-linking Gauss linking Change of magnetic flux through a closed loop: Y.Hirono, DK, Y.Yin PRL117(2016)172301 “large gauge transformation” Gauge dependence of CS number enables its change through magnetic reconnections, and thus the transfer of chirality to fermions which is the chiral anomaly! (QCD: reconnection=instanton) CME from the change of topology General result for an arbitrary change of magnetic flux topology (= CS 3-form): Y.Hirono, DK, Y.Yin PRL117(2016)172301 if we include the electric charge e in the definition of magnetic flux, the pre-factor is the chiral anomaly coefficient that enters the CME current K.Fukushima, DK, H.Warringa ‘08 1. The current would not appear without a change in topology (absence of gauge invariance w.r.t. large gauge transformation). 2. Its magnitude is completely fixed by the change in topological invariant. 3. CME would be absent for fixed μ5 ,such as in the early work by A.Vilenkin ‘80 Chirality transfer from fermions to gauge fields solutions: Chandrasekhar-Kendall states 39 Chirality transfer from fermions to magnetic helicity 40 Self-similar inverse cascade of magnetic helicity driven by CME helical magnetogenesis in the Universe? The link between “helical magnetogenesis” Y. Hirono, DK, Y. Yin , PRD’15 and baryogenesis in Early Universe: N. Yamamoto, PRD’16 DK, E.Shuryak, I.Zahed, arXiv:1906.0480, PRD The CME in relativistic hydrodynamics: The Chiral Magnetic Wave DK, H.-U. Yee, arXiv:1012.6026 [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: 42 M. Mace, N. Mueller, S. Schlichting, S. Sharma, arxiv:1704.05887; PRD’17 Chiral Magnetic Wave in real time! Anomalous transport in real time :axial charge :vector charge B Static U(1) magnetic field in z-dir 43 Chirality in QCD 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 d3xK CS ⌘ o Z Energy of gluon field N CS = -2 -1 0 1 2 instanton sphaleron Is it possible to directly observe these chirality-changing transitions in experiment?44 Can one detect QCD topological