The Golden Age of Chirality and Quantum Mechanics Karl Landsteiner - PowerPoint PPT Presentation

The Golden Age of Chirality and Quantum Mechanics Karl Landsteiner Instituto de Física Teórica UAM-CSIC Theoretical Physics Colloquium , Arizona State University , April 8 th , 2020

Outline •Introduction •Anomalies •Theory of anomalous transport •Realizations • QGP • Weyl semi-metals • Optics •Summary and Outlook

Chiral fluid workshop in Santa Fe, NM, (2018):

“ On the right temple a mauve halfmoon . Suttree turned and lay staring at the ceiling , touching a like mark on his own left temple gently with his fingertips . The ordinary of the second son . Mirror image . Gauche carbon .” “ Gray vines coiled leftward in the northern hemisphere , what winds them shapes the dogwhelk ’ s shell .” “ A dextrocardiac , said the smiling doctor . Your heart ’ s in the right place .” Bryan Giemza: “Mirror Image, Asymmetry, Chirality and Suttree”, Special Issue of the European Journal of American Studies: Cormac McCarthy Between Worlds “For now, su ffi ce it to say that we may be in something of a golden age of chirality, from Breaking Bad to Nobel Prize- winning areas of scientific enquiry.”

林淋良 (Lin Liang) 1424-1500 Imperial painter during Ming Dynasty “Two Chiral Eagles”

Breaking Bad to Nobel Prize CC license, Wikipedia Dextromethamphetamin Levomethamphetamin “crystal meth” Nobel Prize in Chemistry 2016: Bernard L. Feringa [Nobel committee] "for the design and synthesis of (chiral) molecular machines." [from Wikipedia] …“chiral electromagnetic radiation to generate enantioselectivity”… “Zilch”

Homochirality of life Amino acid, all L-isomers Nucleic acid, all R-isomers CC license, Wikipedia

Physics can do better than that: Golden age of chirality starts somewhere here GUTs, Standard Model: Chiral gauge theories (Type IIB, Heterotic strings…) This talk: chiral states (not theories), anomalies and applications

Anomalies Anomaly: Symmetry is not compatible with quantum theory! Weyl fermions H = ± ~ �~ p ρ 5 = Ψ † γ 5 Ψ γ d 1 π 0 2 ⇡ 2 ~ E · ~ dt ⇢ 5 = B γ [Adler], [Bell, Jackiw] 1969

Anomalies Gravitational contribution to Chiral Anomaly: g ρσ 1 D µ J µ 384 ⇡ 2 ✏ µ νρλ R a bµ ν R b 5 = a ρλ A µ g νλ • QM: cannot conserve energy-momentum tensor and axial current as operators • Has a priori nothing to do with gravity: property of QFT in flat space! • Metric = classical sources for energy-momentum tensor • If dynamical metric: decay of neutral pion into gravitons [Kimura] 1969, [Delbourgo, Salam] 1972, [Freund, Eguchi] 1976

Magnetic Field [Miransky, Shokovy, Phys.Rept. 576 (2015) 1-209] p 2 neB + k 2 ω 0 = k z , z , n = 1 , 2 , ... ω = ±

Chiral magnetic effect Chiral Fermions in magnetic field: Landau - levels μ Z µ J = B dk µ 4 π 2 B 2 π = 2 π 0 Many fermion species µ b X X q r a q r b q r q l a q l b q l d abc = J a = d abc 4 π 2 B c c − c r l Anomaly coefficient ! [Vilenkin, 80’ s], [Alekseev, Cheianov, Froehlich] [Shaposhnikov, Giovannini][Fukushima, Kharzeev, Warringa]

Transport & Anomalies Anomaly causes dissipationless currents J R,L = ± µ • Chiral Magnetic Effect ~ 4 ⇡ 2 ~ B ✓ µ 2 ◆ 4 ⇡ 2 + 1 • Chiral Vortical Effect ~ 12 T 2 ~ ! J R,L = ± •Dissipationless Currents! •No Entropy generation! •No quantum corrections! [Vilenkin],[Froehlich, Chaianov], [Fukushima,Kharzeev, Warringa] , [Erdmenger et al.][Batthacharya et al.], [K.L., Megias, Melgar, Pena-Benitez], [K.L., Megias, Pena-Benitez], [Son, Surowka], [ Stephanov, Yee], [Copetti, Fernandez-Pendas, K.L., E. Megias] Nonrenormalization: [Golkar, Son], [Hou, Liu, Ren]

Anomalous effective action δ λ Γ = A λ Non-local local But anomaly can be written as local in 5 dimensions: Z Z δ λ A ∧ F ∧ F = λ F ∧ F ∂ M M Z Z λ ( R (4) ∧ R (4) + D ( K ∧ DK )) d λ R ∧ R = M ∂ M [Haehl, Loganayagam,Rangamani], [Jensen,Loganaygam,Yarom], [di Pietro, Komargodski], [Banerjee, Batthacharya, Battacharyya, Jain, Minwalla, Sharma], [Mañes, Megias, Valle, Vazquez-Mozo]

Anomaly induced currents Thermal equilibrium = constraint on topology Finite T Euclidean: ∂ M = S 1 ⊗ R 3 ds 2 = dr 2 + f ( r ) 2 d ⌧ 2 + g ( r ) 2 d ~ x 2 Smooth geometry in the interior (r=0): β = 1 T f (0) = 0 f 0 (0) = 2 π T Thermal equilibrium = 5D black hole ! [Gibbons, Hawking]

Effective Action Chiral Magnetic Effect, U(1) 3 anomaly Z Z δ A ∧ F ∧ F + 2 δ A ∧ A ∧ F δ Γ CS = 3 M ∂ M “Covariant” current “Bardeen-Zumino” current [Bardeen, Zumino] ‘84 F = Bdx ∧ dy + F 0 r dtdr A r = 0 A 0 = A 0 ( r ) , A 0 | ∂ = µ , A 0 (0) = 0 ∂ r B = 0 δ A = dz 1 J cov = 6 µB Normalisation: 24 π 2 µ One chiral fermion J total = J BZ = − 2 µB 6 π 2 B

Effective Action CME proper: V-A theory Z A ∧ F V ∧ F V Γ = M Z Z δ Γ = 2 δ V ∧ F V ∧ F A + 2 δ V ∧ A ∧ F V M ∂ M CME: J V = 2 µ A B − 2 µ A B = 0 CSE: J A = 2 µ V B Exactly conserved currents have 
 Bloch theorem: to vanish in exact equilibrium [Gynther, K.L., Pena-Benitez, Rebhan], [Kharzeev], [Yamamoto], [Franz, Vazifeh]

Anomaly induced currents Calculate current due to rotation from CS action in slowly rotating black hole ds 2 = dr 2 − f ( r ) 2 [ dt − ( ~ x ] 2 + g ( r ) 2 d ~ x 2 x ) · d ~ ! × ~ Z Z δ A µ h J µ i non − local δ A ^ R ^ R = δ Γ CS = Fixed by ~ J = 4 f 0 (0) 2 ~ ! = 16 ⇡ 2 T 2 ~ ! Topology! [Megias, K.L., Pena-Benitez], [Megias, Melgar, K.L., Pena-Benitez] [Loganayagam, Jensen, Yarom], [de Pietro, Komargodski], [Stone, Kim],

Transport & Anomalies Luttinger: Theory of thermal transport 1964 “ ..if the gravitational field did not exist one could invent it for the purpose of this paper… ” Gravity Thermal transport r Φ g ⌘ � ~ r T ~ T 21st century: Quantum Quantum Gravity Thermal transport 19

Thermal Hall effect ( Γ d Γ + 2 Z 3 Γ 3 ) W bulk = c g bulk ( Γ d Γ + 2 Z 3 Γ 3 ) W boundary = − c g BH Anomaly free: T = 0 ∂ (bulk) = ∂ ( BH ) Only boundary current: J ⊥ E = 16 c g π 2 T ∆ T T T + ∆ T

Gobal anomaly [Golkar, Sethi], [Chowdhyry, David], [Glorioso, Liu, Rajagopal] Compactify on S T × S 1 × S 2 Magnetic flux Z → e i 2 π na Z i Z d 4 x ~ S e ff = A g .d A 48 ⇡ • No global anomaly if a is integer: “fractional” part of CVE • Gravitinos ? [Loganayagam]

Applications • Quark Gluon Plasma • Weyl Semi-Metals • Light

RHIC, Brookhaven LHC, Geneva

Quark gluon plasma 10 15 T!!! strongest Magnetic field in the Universe (QHE: 10 T) + (T ~ 10 12 K) + + + + + J = µ 5 + ⇥ 2 � 2 ⇥ B J + + + - Chiral Magnetic Effect + + + [Fukushima, Kharzeev, McLarren] 
 [Fukushima, Kharzeev, Warringa]

AdS/CFT = 5D geometry = = s = 1 η 4 π [Policastro, Son, Starinets]

Far from equilibrium CME [K.L., E. Lopez, G. Milans del Bosch] 
 [K.L. , J. Fernandez-Pendas] [Ongoing work with S. Tejero-Morales and J. Ghosh] AdS + infalling null dust = AdS Vaidya metric ds 2 = − f ( r, v ) dv 2 + 2 drdv + r 2 d ~ x 2 + q 5 ( v ) 2 ✓ ◆ 1 − 2 m ( v ) f ( r, v ) = r 2 r 4 12 r 6 [Lin, Yee], [Ammon, Grieninger, Jimenez-Alba, Malcedo], [Cartwright, Kaminski], [Cartwritht]

PHYSICAL REVIEW D 100, 126024 (2019) Editors' Suggestion Out-of-equilibrium chiral magnetic effect and momentum relaxation in holography * and Karl Landsteiner † Jorge Fernández-Pendás 4 anom eq τ = 0 . 2 τ = 0 . 5 3 . 8 τ = 1 . 0 τ = 2 . 0 CME @ RHIC 3 . 6 vs 3 . 4 h J i CME @ LHC 3 . 2 3 ??? 2 . 8 2 . 6 0 5 10 15 20 25 v/ τ Final verdict: isobar run results? When?

Weyl Semi-Metal Wikipedia Zr 5 Te Qiang Li (Brookhaven Natl. Lab.), Dmitri E. Kharzeev (Brookhaven Natl. Lab. & TaAs SUNY, Stony Brook), Cheng Zhang, Yuan Huang (Brookhaven Natl. Lab.), I. Pletikosic (Brookhaven Natl. Lab. & Princeton U.), A.V. Fedorov (LBNL, ALS), [Huang, Xu, Belopolski,Hasan] Nature Comm. R.D. Zhong, J.A. Schneeloch, G.D. Gu, T. Valla Hiroyuki Inoue, András Gyenis, Zhijun Wang, Jian Li, Seong Woo Oh, Shan Jiang, Ni Ni, B. Andrei Bernevig,and Ali Yazdani, was published in the March 11, 2016 issue of the journal Science

Weyl semi-metal Linear band touching in Brillouin zone ψ L ψ R TaAs Chiral fermions have to in pairs R and L ! [Nielsen, Ninomiya],

CME in WSMs R L µ R Normal ordered µ L 2 A 5 vacuum 0 Λ 2 � A 5 µ 5 = 1 µ = 1 2( µ L − µ R ) 2( µ R + µ L ) � ⇥ 1 CME: ⇥ µ 5 − A 5 � J = B = 0 0 2 � 2 Covariant and Bardeen-Zumino! [K.L.],[Gorbar, Miransky, Shovkovy, Sukhachov]

NMR and NTMR in WSM [J. Zaanen, “Electrons go with the flow in exotic materials”, S cience Vol. 351, 6277] If WSM is not strongly coupled, hierarchy of scattering times τ inner < τ inter < τ ee Is irrelevant Kills ~ Kills P ⇢ 5 , ✏ 5

NMR and NTMR in WSM NMR = N egative M agneto R esistivity NTMR = N egative T hermo M agneto R esistivity In equilibrium CME vanishes, Induce non-equilibrium steady state 1 B − 1 2 ⇡ 2 ~ E · ~ ⇢ 5 = ⌧ 5 ⇢ 5 ˙ σ + τ 5 B 2 ✓ ◆ J = E 4 π 4 χ 5 [Spivak, Son], [Nielsen, Ninomiya], [Kharzeev]