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E-raamat: Strongly Interacting Matter in Magnetic Fields

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  • Sari: Lecture Notes in Physics 871
  • Ilmumisaeg: 08-Jul-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642373053
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Strongly Interacting Matter in Magnetic FieldsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Physics 871
  • Ilmumisaeg: 08-Jul-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642373053
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The physics of strongly interacting matter in an external magnetic field is presently emerging as a topic of great cross-disciplinary interest for particle, nuclear, astro- and condensed matter physicists.

It is known that strong magnetic fields are created in heavy ion collisions, an insight that has made it possible to study a variety of surprising and intriguing phenomena that emerge from the interplay of quantum anomalies, the topology of non-Abelian gauge fields, and the magnetic field. In particular, the non-trivial topological configurations of the gluon field induce a non-dissipative electric current in the presence of a magnetic field. These phenomena have led to an extended formulation of relativistic hydrodynamics, called chiral magnetohydrodynamics.

Hitherto unexpected applications in condensed matter physics include graphene and topological insulators. Other fields of application include astrophysics, where strong magnetic fields exist in magnetars and pulsars.

Last but not least, an important new theoretical tool that will be revisited and which made much of the progress surveyed in this book possible is the holographic principle - the correspondence between quantum field theory and gravity in extra dimensions.

Edited and authored by the pioneers and leading experts in this newly emerging field, this book offers a valuable resource for a broad community of physicists and graduate students.



Edited and authored by the pioneers and leading experts in this newly emerging field, this book offers a valuable resource for a broad community of physicists and graduate students.
1 Strongly Interacting Matter in Magnetic Fields: A Guide to This Volume
1(12)
Dmitri E. Kharzeev
Karl Landsteiner
Andreas Schmitt
Ho-Ung Yee
1.1 Introduction
1(1)
1.2 Chiral Magnetic Effect and Anomaly-Induced Transport
2(3)
1.3 Phase Structure in a Magnetic Field
5(8)
1.3.1 Phases of QCD in a Magnetic Field
5(3)
1.3.2 Condensed Matter Systems in a Magnetic Field via AdS/CFT
8(3)
References
11(2)
2 Magnetic Catalysis: A Review
13(38)
Igor A. Shovkovy
2.1 Introduction
13(2)
2.2 The Essence of Magnetic Catalysis
15(14)
2.2.1 Dimensional Reduction in a Magnetic Field
15(4)
2.2.2 Magnetic Catalysis in 2 + 1 Dimensions
19(3)
2.2.3 Magnetic Catalysis in 3 + 1 Dimensions
22(1)
2.2.4 Symmetry Breaking as Bound State Problem
23(3)
2.2.5 Analogy with Superconductivity
26(1)
2.2.6 Bound States in Lower Dimensions
27(2)
2.3 Magnetic Catalysis in Gauge Theories
29(8)
2.3.1 Magnetic Catalysis in QED
29(2)
2.3.2 Magnetic Catalysis in QCD
31(2)
2.3.3 Magnetic Catalysis in Graphene
33(4)
2.4 Concluding Remarks
37(14)
Appendix Fermion Propagator in a Magnetic Field
38(3)
References
41(10)
3 Inverse Magnetic Catalysis in Field Theory and Gauge-Gravity Duality
51(36)
Florian Preis
Anton Rebhan
Andreas Schmitt
3.1 Introduction
51(3)
3.2 Chiral Phase Transition in the Nambu-Jona-Lasinio Model
54(13)
3.2.1 Chiral Symmetry Breaking Without External Fields
55(4)
3.2.2 Chiral Symmetry Breaking in the Presence of a Magnetic Field
59(8)
3.3 Chiral Phase Transition in the Sakai-Sugimoto Model
67(15)
3.3.1 Introducing the Model
67(4)
3.3.2 Equations of Motion and Axial Current
71(2)
3.3.3 Semianalytic Solution to the Equations of Motion
73(2)
3.3.4 Broken Chiral Symmetry
75(1)
3.3.5 Symmetric Phase
76(2)
3.3.6 Chiral Phase Transition
78(4)
3.4 Discussion
82(5)
References
83(4)
4 Quark Matter in a Strong Magnetic Background
87(34)
Raoul Gatto
Marco Ruggieri
4.1 Introduction
87(2)
4.2 The PNJL Model with a Magnetic Background
89(4)
4.2.1 The One-Loop Quark Propagator
90(2)
4.2.2 The One-Loop Thermodynamic Potential
92(1)
4.3 Numerical Results
93(7)
4.3.1 Condensates and Dressed Polyakov Loop
94(3)
4.3.2 Entanglement of NJL Coupling and Polyakov Loop
97(3)
4.4 Phase Diagram in the eB-T Plane
100(2)
4.4.1 Comparison with Other Computations
101(1)
4.5 Polarization of the Quark Condensate
102(12)
4.5.1 Non-renormalized Quark-Meson Model Results
105(4)
4.5.2 Results Within the Renormalized QM Model
109(5)
4.6 Conclusions
114(7)
References
116(5)
5 Thermal Chiral and Deconfining Transitions in the Presence of a Magnetic Background
121(22)
Eduardo S. Fraga
5.1 Introduction
121(2)
5.2 Modified Dispersion Relations and Integral Measures
123(2)
5.3 PLSMq Effective Model and the Splitting of the Chiral and Deconfining Transition Lines
125(6)
5.4 Magbag--The Thermal MIT Bag Model in the Presence of a Magnetic Background
131(4)
5.5 Large Nc
135(2)
5.6 Conclusions and Perspectives
137(6)
References
138(5)
6 Electromagnetic Superconductivity of Vacuum Induced by Strong Magnetic Field
143(38)
M.N. Chernodub
6.1 Introduction
143(1)
6.2 Conventional Superconductivity, Vacuum Superconductivity and Schwinger Pair Creation: Differences and Similarities
144(9)
6.2.1 Conventional Superconductivity via Formation of Cooper Pairs
144(2)
6.2.2 Vacuum Superconductivity
146(7)
6.3 Ground State of Vacuum Superconductor
153(24)
6.3.1 Energetic Favorability of the Superconducting State
153(2)
6.3.2 Approaches: Ginzburg-Landau vs Bardeen-Cooper-Schrieffer
155(1)
6.3.3 Example: Ginzburg-Landau Model
156(5)
6.3.4 Superconductivity of Vacuum in Strong Magnetic Field
161(11)
6.3.5 Superconductivity of Vacuum in Nambu-Jona-Lasinio Model
172(5)
6.4 Conclusion
177(4)
References
178(3)
7 Lattice QCD Simulations in External Background Fields
181(28)
Massimo D'Elia
7.1 Introduction
181(2)
7.2 Background Fields on the Lattice
183(7)
7.2.1 Electromagnetic Fields
183(6)
7.2.2 Chromomagnetic Background Fields
189(1)
7.3 Vacuum Properties in Background Fields: Magnetic Catalysis
190(4)
7.4 QCD Phase Diagram in External Fields
194(7)
7.4.1 Deconfinement Transition in a Strong Magnetic Background
195(4)
7.4.2 Deconfinement Transition in a Chromomagnetic Background
199(2)
7.5 More on Gauge Field Modifications in External Electromagnetic Fields
201(4)
7.6 Conclusions
205(4)
References
206(3)
8 P-Odd Fluctuations in Heavy Ion Collisions. Deformed QCD as a Toy Model
209(32)
Ariel R. Zhitnitsky
8.1 Introduction and Motivation
209(2)
8.2 Quantum Anomalies. Effective Lagrangian Approach
211(5)
8.2.1 Charge Separation Effect (CSE)
211(1)
8.2.2 Chiral Magnetic Effect (CME)
212(1)
8.2.3 Chiral Vortical Effect (CVE)
213(3)
8.3 Long Range Order as Seen on the Lattice
216(2)
8.4 Deformed QCD
218(4)
8.4.1 Formulation of the Theory
218(1)
8.4.2 Infrared Description
219(3)
8.5 Domain Walls in Deformed QCD
222(5)
8.5.1 Domain Wall Solution
223(2)
8.5.2 Double Layer Structure
225(2)
8.6 DW in the Presence of Matter Field
227(4)
8.7 CSE, CME, CVE and Related Topological Phenomena in Deformed QCD
231(4)
8.8 Conclusion and Future Directions
235(6)
Appendix
237(2)
References
239(2)
9 Views of the Chiral Magnetic Effect
241(20)
Kenji Fukushima
9.1 Introduction--Discovery of the Chiral Magnetic Effect
241(4)
9.2 Chiral Separation Effect
245(4)
9.3 What Is the Chiral Chemical Potential?
249(2)
9.4 What Really Flows?
251(5)
9.5 My Outlook
256(5)
References
257(4)
10 The Chiral Magnetic Effect and Axial Anomalies
261(34)
Gokce Basar
Gerald V. Dunne
10.1 Dirac Operators, Dimensional Reduction and Axial Anomalies
261(9)
10.1.1 Lowest Landau Level Projection
261(2)
10.1.2 Schur Decomposition of Dirac Propagator
263(2)
10.1.3 Currents and Anomalies in the Lowest Landau Level Projection
265(2)
10.1.4 Chiral Magnetic Effect and the Schwinger Effect
267(1)
10.1.5 Maxwell-Chern-Simons Theory and the Schwinger Model
268(2)
10.2 Chiral Magnetic Spiral
270(6)
10.2.1 Basic Setup and Dimensional Reduction
271(2)
10.2.2 Life in Two-Dimensions
273(3)
10.3 Fermions in an Instanton and Magnetic Field Background
276(14)
10.3.1 Euclidean Dirac Operator
277(2)
10.3.2 Magnetic Field Background
279(1)
10.3.3 Instanton Background
280(1)
10.3.4 Combined Instanton and Magnetic Field Background
281(2)
10.3.5 Large Instanton Limit: Covariantly Constant SU(2) Instanton and Constant Abelian Magnetic Field
283(2)
10.3.6 Dirac Spectrum in the Strong Magnetic Field Limit
285(2)
10.3.7 Physical Picture: Competition Between Spin and Chirality Projection
287(1)
10.3.8 Matrix Elements and Dipole Moments
287(3)
10.4 Conclusions
290(5)
References
291(4)
11 Chiral Magnetic Effect in Hydrodynamic Approximation
295(36)
Valentin I. Zakharov
11.1 Introduction
295(6)
11.2 Non-renormalization Theorems
301(13)
11.2.1 Non-renormalization Theorems in Thermodynamic Approach
301(3)
11.2.2 Non-renormalization Theorems in Geometric Approach
304(4)
11.2.3 Non-renormalization Theorems in Diagrammatic Approach
308(3)
11.2.4 Non-renormalization Theorems in Effective Field Theories
311(3)
11.2.5 Concluding Remarks
314(1)
11.3 Hydrodynamic Chiral Effects as Quantum Phenomena
314(9)
11.3.1 Non-dissipative Currents
314(2)
11.3.2 Low-Dimensional Defects
316(1)
11.3.3 Relativistic Superfluidity
317(3)
11.3.4 Zero Modes
320(2)
11.3.5 Concluding Remarks
322(1)
11.4 Conclusions
323(8)
References
327(4)
12 Remarks on Decay of Defects with Internal Degrees of Freedom
331(10)
A. Gorsky
12.1 Introduction
331(1)
12.2 Decay of Axion-Like Domain Walls in D = 3 + 1 Theories
332(3)
12.3 Decays of Mesonic Walls
335(2)
12.3.1 Decay of π0 Domain Walls
335(1)
12.3.2 Wall Decay in QCD at High Density
336(1)
12.4 Nonabelian String Decay
337(1)
12.5 Summary
338(3)
References
339(2)
13 A Chiral Magnetic Effect from AdS/CFT with Flavor
341(36)
Carlos Hoyos
Tatsuma Nishioka
Andy O'Bannon
13.1 Introduction
341(4)
13.2 The Theory in Question
345(4)
13.3 Chiral Magnetic Effect from Spinning Probe Branes
349(17)
13.3.1 Solutions at Zero Temperature
356(6)
13.3.2 Solutions at Finite Temperature
362(4)
13.4 Loss Rates of Axial Charge and of Energy
366(4)
13.5 Summary and Discussion
370(7)
References
373(4)
14 Lattice Studies of Magnetic Phenomena in Heavy-Ion Collisions
377(10)
P.V. Buividovich
M.I. Polikarpov
O.V. Teryaev
14.1 Introduction
377(1)
14.2 Chiral Magnetic Effect
378(4)
14.3 Induced Conductivity and Abnormal Dilepton Yield
382(2)
14.4 Conclusions
384(3)
References
384(3)
15 Chiral Magnetic Effect on the Lattice
387(12)
Arata Yamamoto
15.1 Introduction
387(1)
15.2 Basics of the Lattice Simulation
388(2)
15.3 Lattice Simulation with a Topological Background
390(3)
15.4 Lattice Simulation with a Chiral Chemical Potential
393(3)
15.5 Conclusion
396(3)
References
397(2)
16 Magnetism in Dense Quark Matter
399(34)
Efrain J. Ferrer
Vivian de la Incera
16.1 Introduction
399(1)
16.2 Magnetic Fields in Compact Stars
399(2)
16.3 Magnetism in Spin-Zero Color Superconductivity
401(1)
16.4 The Magnetic CFL Phase
402(6)
16.5 Magnetoelectric Effect in Cold-Dense Matter
408(5)
16.6 Paramagnetism in Color Superconductivity
413(3)
16.7 Magnetic Phases in CFL Matter
416(1)
16.8 Equation of State of the MCFL Phase
417(7)
16.8.1 Covariant Structure of the Energy-Momentum Tensor in a Magnetized System
419(2)
16.8.2 MCFL Thermodynamic Potential
421(1)
16.8.3 EoS in a Magnetic Field
422(2)
16.9 Astrophysical Implications
424(9)
16.9.1 Low-Energy Physics
424(2)
16.9.2 Boosting Stellar Magnetic Fields via an Internal Mechanism
426(1)
16.9.3 Stability of Magnetized Quark Stars
427(2)
References
429(4)
17 Anomalous Transport from Kubo Formulae
433(36)
Karl Landsteiner
Eugenio Megias
Francisco Pena-Benitez
17.1 Introduction
433(3)
17.2 Anomalies and Hydrodynamics
436(14)
17.2.1 Anomalies
436(4)
17.2.2 Chemical Potentials for Anomalous Symmetries
440(7)
17.2.3 Contributions to the Kubo Formulae
447(3)
17.3 Weyl Fermions
450(7)
17.3.1 Chiral Vortical Conductivity
451(3)
17.3.2 Chiral Magnetic Conductivity
454(1)
17.3.3 Conductivities for the Energy Flux
455(1)
17.3.4 Summary and Specialization to the Group U(1)v x U(1)A
456(1)
17.4 Holographic Model
457(7)
17.4.1 Notation and Holographic Anomalies
457(2)
17.4.2 Applying Kubo Formulae and Linear Response
459(5)
17.5 Conclusion and Outlook
464(5)
Appendix 1 Boundary Counterterms
465(1)
Appendix 2 Equations of Motion for the Shear Sector
466(1)
References
466(3)
18 Quantum Criticality via Magnetic Branes
469(34)
Eric D'Hoker
Per Kraus
18.1 Introduction
469(2)
18.2 Basic Gauge Theory Dynamics
471(2)
18.2.1 Effective Low Energy Degrees of Freedom
471(1)
18.2.2 Luttinger Liquids
472(1)
18.3 Holographic Dual Set-Up
473(2)
18.3.1 Field Equations and Structure of the Solutions
474(1)
18.3.2 Boundary Stress Tensor and Current
475(1)
18.4 The Purely Magnetic Brane: Zero Charge Density
475(7)
18.4.1 The Purely Magnetic Brane at T = 0
475(1)
18.4.2 RG Flow and Thermodynamics
476(2)
18.4.3 Calculation of Current-Current Correlators at T = 0
478(1)
18.4.4 Method of Overlapping Expansions
479(1)
18.4.5 Current Two-Point Correlators
480(1)
18.4.6 Maxwell-Chern-Simons Holography in AdS3
480(1)
18.4.7 Effective Conformal Field Theory and Double-Trace Operators
481(1)
18.4.8 Stress Tensor Correlators and Emergent Virasoro Symmetry
482(1)
18.5 Holographic Dual Solutions for Non-zero Charge Density
482(10)
18.5.1 Reduced Field Equations
483(1)
18.5.2 Near-Horizon Schrodinger Geometry
484(1)
18.5.3 The Charged Magnetic Brane Solution
484(1)
18.5.4 Regularity of the Solutions
485(1)
18.5.5 Existence of a Critical Magnetic Field
486(1)
18.5.6 Low T Thermodynamics for B > Bc
487(1)
18.5.7 Low T Thermodynamics for B = Bc
488(1)
18.5.8 Scaling Function in the Quantum Critical Region
489(1)
18.5.9 Numerical Completion of the Holographic Phase Diagram
490(1)
18.5.10 Correlators at Non-zero Charge Density
491(1)
18.5.11 Comments on Stability
492(1)
18.6 Quantum Criticality in 2 + 1 Dimensions
492(5)
18.6.1 Field Equations and Structure of the Solutions
493(1)
18.6.2 Horizon and Asymptotic Data, Physical Quantities
494(1)
18.6.3 Flows Towards the Electric IR Fixed Point
495(1)
18.6.4 Flows Towards the Magnetic IR Fixed Point
495(1)
18.6.5 Flows Towards the Lifshitz IR Fixed Point
496(1)
18.6.6 The Full Phase Diagram
496(1)
18.7 Relation with Quantum Criticality in Condensed Matter
497(6)
18.7.1 Meta-Magnetic Transitions in Strontium Ruthenates
497(2)
18.7.2 Relation to Hertz-Millis Theory
499(1)
References
500(3)
19 Charge-Dependent Correlations in Relativistic Heavy Ion Collisions and the Chiral Magnetic Effect
503(34)
Adam Bzdak
Volker Koch
Jinfeng Liao
19.1 Introduction
503(4)
19.1.1 The Chiral Magnetic Effect in Brief
504(1)
19.1.2 Hunting for the CME in Heavy Ion Collisions
505(2)
19.2 The Charge-Dependent Correlation Measurements
507(9)
19.2.1 General Considerations Concerning Azimuthal Correlation Measurements
508(3)
19.2.2 Measuring the Charge Separation Through Azimuthal Correlations
511(3)
19.2.3 The Qc1 Vector Analysis for Measuring the Charge Separation
514(2)
19.3 Interpretation of the Available Data
516(4)
19.4 Discussion of Various Background Contributions
520(13)
19.4.1 General Relation
521(2)
19.4.2 Transverse Momentum Conservation
523(3)
19.4.3 AMPT Model
526(2)
19.4.4 Local Charge Conservation
528(1)
19.4.5 Decomposition of Flow-Induced and Flow-Independent Contributions
529(3)
19.4.6 Suppression of Elliptic-Flow-Induced Correlations
532(1)
19.5 Summary and Conclusions
533(4)
References
534(3)
20 Holography, Fractionalization and Magnetic Fields
537(18)
Tameem Albash
Clifford V. Johnson
Scott McDonald
20.1 Charged Ideal Fluid with a Magnetic Field
540(6)
20.1.1 Gravity Background
540(3)
20.1.2 Density of States for (3 + 1)-Dimensional Fermions in a Magnetic Field
543(2)
20.1.3 Action Calculation
545(1)
20.2 The Role of the Dilaton
546(3)
20.3 Solutions with Stars
549(2)
20.3.1 Mesonic Phase: Star in the Infra-Red
549(1)
20.3.2 Partially Fractionalized Phases: Star Outside Horizon
550(1)
20.4 Concluding Remarks
551(4)
References
552(3)
21 Holographic Description of Strongly Correlated Electrons in External Magnetic Fields
555(36)
E. Gubankova
J. Brill
M. Cubrovic
K. Schalm
P. Schijven
J. Zaanen
21.1 Introduction
555(4)
21.2 Holographic Fermions in a Dyonic Black Hole
559(5)
21.2.1 Dyonic Black Hole
559(3)
21.2.2 Holographic Fermions
562(2)
21.3 Magnetic Fields and Conformal Invariance
564(2)
21.3.1 The Near-Horizon Limit and Dirac Equation in AdS2
564(2)
21.4 Spectral Functions
566(6)
21.4.1 Relating to the ARPES Measurements
566(2)
21.4.2 Magnetic Crossover and Disappearance of the Quasiparticles
568(1)
21.4.3 Density of States
569(3)
21.5 Fermi Level Structure at Zero Temperature
572(8)
21.5.1 Dirac Equation with m = 0
572(3)
21.5.2 Magnetic Effects on the Fermi Momentum and Fermi Velocity
575(5)
21.6 Hall and Longitudinal Conductivities
580(6)
21.6.1 Integer Quantum Hall Effect
581(4)
21.6.2 Fractional Quantum Hall Effect
585(1)
21.7 Conclusions
586(5)
References
588(3)
22 A Review of Magnetic Phenomena in Probe-Brane Holographic Matter
591
Oren Bergman
Johanna Erdmenger
Gilad Lifschytz
22.1 Introduction
591(2)
22.2 The D3-D7 Model
593(8)
22.2.1 Brane Construction
593(3)
22.2.2 Finite Temperature
596(1)
22.2.3 Magnetic Catalysis
597(2)
22.2.4 Superfluid
599(2)
22.3 The D4-D8-(Sakai-Sugimoto) Model
601(13)
22.3.1 Basics
601(3)
22.3.2 Finite Density and Background Fields
604(2)
22.3.3 Magnetic Catalysis of Chiral Symmetry Breaking
606(1)
22.3.4 Anomalous Currents
607(2)
22.3.5 The Pion Gradient Phase
609(3)
22.3.6 Magnetic Phase Transition
612(2)
22.4 The D3-D7' Model
614
22.4.1 Stable Embeddings
614(2)
22.4.2 Finite Density and Background Fields
616(2)
22.4.3 Quantum Hall States
618(1)
22.4.4 Fermi-Like Liquid
619(2)
References
621
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