World-line construction of a covariant chiral kinetic theory Niklas - - PowerPoint PPT Presentation

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World-line construction of a covariant chiral kinetic theory Niklas - - PowerPoint PPT Presentation

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World-line construction of a covariant chiral kinetic theory Niklas Mueller with Raju Venugopalan, arXiv:1701.03331, 1702.01233; and with Raju Venugopalan and Yi Yin, in prep. Cold Quantum Coffee Heidelberg, 09.05.2017 Outline of this talk

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World-line construction of a covariant chiral kinetic theory

Niklas Mueller

with Raju Venugopalan, arXiv:1701.03331, 1702.01233; and with Raju Venugopalan and Yi Yin, in prep.

Cold Quantum Coffee Heidelberg, 09.05.2017

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Outline of this talk

1. Motivation for a chiral kinetic theory 2. Things that should make you suspicious 3. World line formulation of the effective action 4. Equations of motion and what Berry's phase really is 5. Towards the big picture

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Motivation

  • What do heavy ion collisions tell us about

fundamental symmetries?

Axial Imbalance Large Magnetic Fields Electric currents (observable) local CP-odd domains

+ =

Kharzeev, McLerran, Warringa 2007

The Chiral Magnetic Effect P- and CP- odd phenomena in QCD – anomalies and topology

2

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Motivation

  • Topological and anomalous phenomena

STAR; PRL 103 (2009) 251601; PRC 81 (2010) 54908

CMS, arxiv 1610.00263

2009: initial excitement, charge correlations and signs as predicted (?) today: not so sure Experimental verification very hard:

  • qualitative predictions do exist
  • quantitative understanding of signal or background do not

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Motivation

  • Topological and anomalous phenomena

Prithwish Tribedy (STAR) at QM 2017

Background: a difficult task

  • Signal and background have similar centrality dependence

Paul Soerensen (STAR) at QM 2017

  • Local charge conservation (Schlichting et al.)
  • ….

Isobar run coming soon! (Chiral Magnetic Effect Task Force Report, arXiv:1605.01413 [hep-ph] |) But: THEORETICAL understanding needed! 4 Npart Y/<Y>max

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CGC colliding nuclei flux tubes

  • ver-occupied

plasma kinetic regime hydrodynamic regime

  • S. Schlichting 2016

non-equilibrium anomalous fermion production from coherent fields (Tanji et al. 2016) and sphaleron transitions (Mace et al. 2016) large magnetic fields present Anomalous Transport (CME, CSE and CMW)

?

Subsequent interactions in the fire ball, axial transport and relaxation weak to strong coupling

classical statistical simulations + fermions chiral kinetic theory anomalous hydrodynamics

Motivation

  • The limits of what we can calculate, and

where the interesting physics lives

T h e r ma l i z a t i

  • n

? ? ?

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Motivation

  • We need a chiral kinetic theory

Always a challenge, as natural to formulate in first quantization (point-particles), whereas most of our modern concepts (anomalies etc.) are in second quantization (fields)

Berry connection and chiral kinetic theory

Son and Yamamoto, Stephanov and Yin (2012)

Berry phase: Berry monopole: Weyl equation: Effective theory in the adiabatic limit, describing excitations near the fermion surface: Claim: accounts for the dynamics of the anomaly by some continuity arguments (incompressibility of phase space) Geometric only in the adiabatic limit 6

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Chiral Kinetic Theory

  • a 'hot' topic

Big excitement across many communities!

Son,Yamamoto, PRL109 (2012), 181602; PRD87 (2013) 085016, Stephanov, Yin, PRL109 (2012) 162001, Chen, Son, Stephanov, Yee, Yin, PRL 113 (2014) 182302, Chen, Son, Stephanov, PRL115 (2015) 021601, Chen,Pu,Wang,Wang, PRL110 (2013) 26230, Gao, Liang, Pu, Wang, Wang, PRL109 (2012) 232301, Stone, Dwivedi,Zhou, PRD91 (2015) 025004, Zahed, PRL109 (2012) 091603; Basar, Kharzeev,Zahed, PRL111 (2013)161601 Stephanov,Yi,Yin,PRD91 (2015) 125014, Manuel, Torres-Rincon, PRD 90, 076007 (2014) …

8+ PRLs in last 5 years! Relation of Berry phase and the anomaly? In Fujikawa's words ... and ... 7

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Chiral Kinetic Theory

  • a closer look

Relation of Berry phase and the anomaly?

Things to consider

? adiabatic approximation (absence of level crossing)

  • vs. level crossing interpretation of the anomaly (Fujikawa 2005)

→ robustness of the anomaly and approximations

? adiabatic limit and large chemical potential not applicable to ultra-relativistic heavy ion

collisions

? 'classical' description of spinning particles

→ spin connection vs 'where does the anomaly really come from'

? Lorentz covariance? scattering kernels, side jumps etc.

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World line formulation

  • f the effective action

some rather old stuff (Schwinger, Feynman) … re-discovered many times (Strassler) … and some pioneers of the modern interpretation from Heidelberg (Schmidt, Schubert)! ...

  • ne-loop effective actions

quantum mechanical particle, quantized on closed loop (world line)

  • anomalies from the

path integral measure

  • Witten & Alvarez-Gaume

(1983): fermionic determinant and anomalies

→ path integral representation

  • f the index of the Dirac
  • perator
  • natural interpretation of

pseudo-classical approximation (quasi-particles)

  • Lorentz-covariant
  • Gauge covariant

Will show you: 1st ingredient: integral- representation of the logarithm 9

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World line formulation

  • f the effective action

WARNING! EQUATIONS! Matter + Gauge fields:

Fermions (do not expect a complete derivation here!)

anomalies live here

real part: 2nd ingredient: representation of the trace

  • ver Gamma matrices via

fermionic coherent states 10

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Equations of motion

After many manipulations the real part of the effective action is written as a QM path integral: = no approximations! (QFT!!!) The quasi-particle limit is very illustrative in this formulation … → the saddle point approximation gives: These are the covariant form of the famous Bargman-Michel-Telegdi and Wong's equations (when written down for QCD)! fermionic variables world-line So where is the anomaly? And where would Berry's phase be? 11

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The origin of Berry's phase ...

Adiabatic (and non-relativistic) approximation of the world-line path integral gives Berry's phase It is pretty clear what the role of Berry's phase is: → spin transport along the world-line of the particle → related to defining the 'moving frame' for the spin variables Most importantly: It is not robust! (Part of the dynamics away from adiabatic approx.)

… we got it from the real part of the effective action … … the anomaly stems from the imaginary part (more soon) … what Berry's phase has to do with the anomaly:

… not much, really ...

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So where does the anomaly then come from?

Reminder: Alvarez-Gaume and Witten 80's (Euclidean):

  • Imaginary part of the effective action = phase of the fermion determinant

is ill defined!!! → ORIGIN of the anomaly

  • a naïve heat-kernel / world-line representation of the imaginary part of the

effective action is possible – ONLY if we break chiral symmetry explicitly:

anomalies live here

Where did this come from? → path integral representation for imaginary part:

  • remember quantization on closed loop! (c.f. Schmidt, Schubert, D'Hoker, Gagne)
  • for the imaginary part: periodic boundary conditions for fermionic variables

→ zero modes = source of the anomaly (Polyakov) 13

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A small recap'

We have shown:

  • The identification of the topology of Berry's phase with that of the

anomaly in current literature (8+ PRLs) is a misconception.

  • The origin of the anomaly can be understood using world-lines to arise

from fermionic zero modes in the path integral in first quantization

  • This allows to derive a kinetic theory (first quantization, particles!) from

first principles → consistent derivation of anomalies → Lorentz covariant → gauge covariant The world-line technique is extremely powerful! (Fun fact: Bern and Kosower have

derived it from string theory in the infinite string tension limit.)

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CGC colliding nuclei flux tubes

  • ver-occupied

plasma kinetic regime hydrodynamic regime

  • S. Schlichting 2016

non-equilibrium anomalous fermion production from coherent fields (Tanji et al. 2016) and sphaleron transitions (Mace et al. 2016) large magnetic fields present Anomalous Transport (CME, CSE and CMW)

?

Subsequent interactions in the fire ball, axial transport and relaxation weak to strong coupling

classical statistical simulations + fermions chiral kinetic theory anomalous hydrodynamics

T h e r ma l i z a t i

  • n

? ? ?

The big picture

  • and other cool stuff

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The big picture

  • and other cool stuff

World-lines: a powerful tool to derive kinetic theories from first principles! Some work ahead, but straightforward: 16

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The big picture

  • and other cool stuff

Quantitative understanding of the Chiral Magnetic Effect. Neutron stars and supernovae: understanding helicity transport, neutrinos and large helical magnetic fields (see

Yamamoto, Kaplan, etc.)

Spin structure of the nucleon.

  • ne bosonic 'field' for every dimension (Lorentz-covariant)

→ Sound interesting, cold atom friends?

also note: can go beyond one-loop. And yes, it is what you think it is: scatterings of world-

  • lines. (ask M. Schmidt for more details!)

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