Gauge/Gravity Duality and Strongly Coupled Matter. Johanna Erdmenger. Max Planck-Institut für Physik, München

Transcription

1 .. Gauge/Gravity Duality and Strongly Coupled Matter Johanna Erdmenger Max Planck-Institut für Physik, München 1

2 Motivation Matter under Extreme Conditions Strongly Coupled Matter

3 Motivation Matter under Extreme Conditions Strongly Coupled Matter New theoretical approaches welcome to complement existing ones In particular for dynamical processes, at finite density,...

4 Motivation Matter under Extreme Conditions Strongly Coupled Matter New theoretical approaches welcome to complement existing ones In particular for dynamical processes, at finite density,... Gauge/Gravity Duality

5 Motivation Matter under Extreme Conditions Strongly Coupled Matter New theoretical approaches welcome to complement existing ones In particular for dynamical processes, at finite density,... Gauge/Gravity Duality maps strongly coupled gauge theories to weakly coupled gravity theories originates from string theory 2

6 Gauge/Gravity Duality Gauge/gravity duality: Generalizations of AdS/CFT correspondence AdS: Anti-de Sitter space, CFT: Conformal field theory

7 Gauge/Gravity Duality Gauge/gravity duality: Generalizations of AdS/CFT correspondence AdS: Anti-de Sitter space, CFT: Conformal field theory Gauge/Gravity Duality is a powerful tool for

8 Gauge/Gravity Duality Gauge/gravity duality: Generalizations of AdS/CFT correspondence AdS: Anti-de Sitter space, CFT: Conformal field theory Gauge/Gravity Duality is a powerful tool for uncovering universal behaviour

9 Gauge/Gravity Duality Gauge/gravity duality: Generalizations of AdS/CFT correspondence AdS: Anti-de Sitter space, CFT: Conformal field theory Gauge/Gravity Duality is a powerful tool for uncovering universal behaviour creating new links between strongly correlated quantum liquids quark-gluon plasma ultracold atoms neutron matter

10 Gauge/Gravity Duality Gauge/gravity duality: Generalizations of AdS/CFT correspondence AdS: Anti-de Sitter space, CFT: Conformal field theory Gauge/Gravity Duality is a powerful tool for uncovering universal behaviour creating new links between strongly correlated quantum liquids quark-gluon plasma ultracold atoms neutron matter studying phase transitions (thermal and quantum)

11 Gauge/Gravity Duality Gauge/gravity duality: Generalizations of AdS/CFT correspondence AdS: Anti-de Sitter space, CFT: Conformal field theory Gauge/Gravity Duality is a powerful tool for uncovering universal behaviour creating new links between strongly correlated quantum liquids quark-gluon plasma ultracold atoms neutron matter studying phase transitions (thermal and quantum) Top-down approach: Solve equations of motion in 10d gravity 3

12 1. Basics of Gauge/Gravity Duality Outline

13 Outline 1. Basics of Gauge/Gravity Duality 2. An Example for Applications: Superconductivity/Superfluidity at finite isospin density 4

14 1. Basics of Gauge/Gravity Duality 5

15 AdS/CFT correspondence (Maldacena 1997) SU(N) gauge theory (Quantum) Duality String Theory Gravity (Quantum) Saddle point approximation Large N gauge theory Duality Classical Gravity 6

16 String theory origin of AdS/CFT correspondence D3 branes in 10d duality AdS x S5 5 near-horizon geometry Low-energy limit N = 4 SU(N) theory in four dimensions (N ) Supergravity on AdS 5 S 5 7

17 AdS/CFT correspondence (Maldacena 1997) AdS: Anti-de Sitter space in d = 5 CFT: conformal field theory in d = 4 Symmetry properties coincide Dictionary Gauge invariant operators in field theory Fields in gravity theory 8

18 Generalizations of the AdS/CFT Correspondence

19 Generalizations of the AdS/CFT Correspondence 1. Symmetry requirements are relaxed in a controlled way

20 Generalizations of the AdS/CFT Correspondence 1. Symmetry requirements are relaxed in a controlled way RG flows Theories with confinement similar to QCD

21 Generalizations of the AdS/CFT Correspondence 1. Symmetry requirements are relaxed in a controlled way RG flows Theories with confinement similar to QCD Finite temperature and finite density

22 Generalizations of the AdS/CFT Correspondence 1. Symmetry requirements are relaxed in a controlled way RG flows Theories with confinement similar to QCD Finite temperature and finite density 2. More degrees of freedom are added (Example: quarks)

23 Generalizations of the AdS/CFT Correspondence 1. Symmetry requirements are relaxed in a controlled way RG flows Theories with confinement similar to QCD Finite temperature and finite density 2. More degrees of freedom are added (Example: quarks) 3. Non-relativistic theories 9

24 Quarks (fundamental fields) within the AdS/CFT correspondence Adding D7 brane probe: Babington, J.E., Evans, Guralnik, Kirsch PRD D3 X X X X D7 X X X X X X X X π pseudoscalar meson mass: From fluctuations of hypersurface ρ vector meson mass: From fluctuations of gauge field on hypersurface 10

25 Comparison to lattice gauge theory Mass of ρ meson as function of π meson mass 2 (for N ) m Ρ m ρ SU(2) SU(3) SU(4) SU(6) N = inf m Π m π J.E., Evans, Kirsch, Threlfall 07, review EPJA Lattice: Lucini, Del Debbio, Patella, Pica 07 AdS/CFT result: m ρ (m π ) m ρ (0) = ( ) 2 mπ m ρ (0) Lattice result (from Bali, Bursa 08): slope ±

26 Part II: Application Example Superconductivity/Superfluidity 12

27 Superconductivity/Superfluidity Superfluidity in quark-gluon plasma: Instability at finite isospin density ρ meson condensate, flavour degrees of freedom can move without friction

28 Superconductivity/Superfluidity Superfluidity in quark-gluon plasma: Instability at finite isospin density ρ meson condensate, flavour degrees of freedom can move without friction Moreover: Global U(1) toy model for electromagnetism

29 Superconductivity/Superfluidity Superfluidity in quark-gluon plasma: Instability at finite isospin density ρ meson condensate, flavour degrees of freedom can move without friction Moreover: Global U(1) toy model for electromagnetism Fermionic excitations in superfluid Excitations near zeroes of the energy gap (order parameter) 13

30 Gauge/Gravity Duality at Finite Temperature

31 Gauge/Gravity Duality at Finite Temperature N = 4 Super Yang-Mills theory at finite temperature is dual to AdS black hole Witten 1998

32 Gauge/Gravity Duality at Finite Temperature N = 4 Super Yang-Mills theory at finite temperature is dual to AdS black hole Witten 1998 Toy model for quark-gluon plasma 14

33 Quarks in Gauge/Gravity Duality at Finite Temperature D7 brane embedding in black hole background Minkowski phase First order phase transition Black hole phase Babington, J.E., Evans, Guralnik, Kirsch Mateos, Myers, Thomson 15

34 Masses and decay widths of mesons Standard procedure in D3/D7: Mateos, Myers et al 2003 Meson masses calculated from linearized fluctuations of D7 embedding Fluctuations: δw(x, ρ) = f(ρ)e i( k x ωt), M 2 = k 2

35 Masses and decay widths of mesons Standard procedure in D3/D7: Mateos, Myers et al 2003 Meson masses calculated from linearized fluctuations of D7 embedding Fluctuations: δw(x, ρ) = f(ρ)e i( k x ωt), M 2 = k 2 For black hole embeddings, ω develops negative imaginary part damping decay width

36 Masses and decay widths of mesons Standard procedure in D3/D7: Mateos, Myers et al 2003 Meson masses calculated from linearized fluctuations of D7 embedding Fluctuations: δw(x, ρ) = f(ρ)e i( k x ωt), M 2 = k 2 For black hole embeddings, ω develops negative imaginary part damping decay width Quasinormal modes of D7 brane fluctuations determine meson mass and width Landsteiner, Hoyos, Montero 2006

37 Masses and decay widths of mesons Standard procedure in D3/D7: Mateos, Myers et al 2003 Meson masses calculated from linearized fluctuations of D7 embedding Fluctuations: δw(x, ρ) = f(ρ)e i( k x ωt), M 2 = k 2 For black hole embeddings, ω develops negative imaginary part damping decay width Quasinormal modes of D7 brane fluctuations determine meson mass and width Landsteiner, Hoyos, Montero 2006 Excitations in strongly coupled system 16

38 Quasinormal Modes and Spectral Functions R(w, 0) d = 0.25 χ 0 = n = 0 n = 1 n = 2 n = Minkowski phase Mesons stable Normal modes real w R(w, 0) R0 250 d = 0.25 n = 0 n = 1 n = 2 n = χ 0 = Black hole phase Mesons decay Quasinormal modes complex w 17

39 Finite U(1) baryon density

40 Finite U(1) baryon density Baryon density n B and U(1) chemical potential µ from non-trivial profile for gauge field time component: Ā 0 (ρ) µ + d ρ 2, d = 2 5/2 N f λt 3 n B Mateos, Myers, Matsuura et al At finite baryon density, all embeddings are black hole embeddings 18

41 Phase diagram with finite U(1) baryon density Phase diagram: 1 d = grey region: n B = 0 white region: n B 0 µq/mq d = 0 d = 0.25 d = T/ M

42 Isospin chemical potential and density Embed two coincident D7-branes into AdS-Schwarzschild gauge fields A µ = A a µ σ a u(2) = u(1) B su(2) I Finite isospin density: A Explicit breaking to u(1) 3

43 Isospin chemical potential and density Embed two coincident D7-branes into AdS-Schwarzschild gauge fields A µ = A a µ σ a u(2) = u(1) B su(2) I Finite isospin density: A Explicit breaking to u(1) 3 Field theory described: N = 4 Super Yang-Mills plus two flavors of fundamental matter at finite temperature and finite isospin density 20

44 ρ meson condensation Above a critical isospin density, a new phase forms J.E., Kaminski, Kerner, Rust

45 ρ meson condensation Above a critical isospin density, a new phase forms J.E., Kaminski, Kerner, Rust New phase is unstable 21

46 Quasinormal modes Instability: Im ω Imw Rew Re ω 22

47 A new ground state forms There is a new solution to the equations of motion with non-zero vev for A 1 3σ 1 in addition to the non-zero A 3 0σ 3

48 A new ground state forms There is a new solution to the equations of motion with non-zero vev for A 1 3σ 1 in addition to the non-zero A 3 0σ 3 A 3 0 = µ d 3 0 2πα ρ H ρ , A1 3 = d 3 1 2πα ρ H ρ

49 A new ground state forms There is a new solution to the equations of motion with non-zero vev for A 1 3σ 1 in addition to the non-zero A 3 0σ 3 A 3 0 = µ d 3 0 2πα ρ H ρ , A1 3 = d 3 1 2πα ρ H ρ Pole structure: ÈË Ö Ö ÔÐ Ñ ÒØ ÁÑÛ Ê Û Ò ½ Ò ½ Ò ¼ Ò ¼ Ò ¼ 23

50 Superconductivity Ammon, J.E., Kaminski, Kerner , The new ground state has properties known from superconductors: infinite DC conductivity, gap in the AC conductivity second order phase transition, critical exponent of 1/2 (mean field) a remnant of the Meissner Ochsenfeld effect 24

51 Superfluidity and Superconductivity Order parameter d 1 3 ψ u γ 3 ψ d + ψ d γ 3 ψ u + bosons 0 ρ meson condensate (p-wave symmetry)

52 Superfluidity and Superconductivity Order parameter d 1 3 ψ u γ 3 ψ d + ψ d γ 3 ψ u + bosons 0 ρ meson condensate (p-wave symmetry) Spontaneous breaking of (global) U(1) 3

53 Superfluidity and Superconductivity Order parameter d 1 3 ψ u γ 3 ψ d + ψ d γ 3 ψ u + bosons 0 ρ meson condensate (p-wave symmetry) Spontaneous breaking of (global) U(1) 3 ρ meson condensate at finite isospin density discussed in QCD literature Son, Stephanov; Splittorff; Sannino...

54 Superfluidity and Superconductivity Order parameter d 1 3 ψ u γ 3 ψ d + ψ d γ 3 ψ u + bosons 0 ρ meson condensate (p-wave symmetry) Spontaneous breaking of (global) U(1) 3 ρ meson condensate at finite isospin density discussed in QCD literature Son, Stephanov; Splittorff; Sannino... Flavour superfluid

55 Superfluidity and Superconductivity Order parameter d 1 3 ψ u γ 3 ψ d + ψ d γ 3 ψ u + bosons 0 ρ meson condensate (p-wave symmetry) Spontaneous breaking of (global) U(1) 3 ρ meson condensate at finite isospin density discussed in QCD literature Son, Stephanov; Splittorff; Sannino... Flavour superfluid Within QCD: Superconductivity in presence of magnetic field Chernodub

56 Thermodynamics Flavour contribution to Grand potential vs. temperature W T T c 26

57 Conductivity Frequency-dependent conductivity σ(ω) = i ω GR (ω) G R retarded Green function for fluctuation a Re σ w w = ω/(2πt ) T/T c : Black:, Red: 1, Orange: 0.5, Brown: (Vanishing quark mass) Interpretation: Frictionless motion of mesons through plasma 27

58 Meissner effect À ¼ Ñ ÒØ Ì ½ ¼ Lower phase: magnetic field and condensate coexist Upper phase: condensate vanishes 28

59 Quantum phase transition Turn on both isospin and baryon chemical potential  ½ Ü ¼ Õ ¾ Ì Á  ½ Ü ¼ Á Example for Quantum Phase Transition Figure by Patrick Kerner 29

60 Quantum Phase Transition Movement of quasinormal modes 30

61 Quantum phase transition Phase diagrams Quantum Phase Transition Superconductor 31

62 Fermionic excitations in holographic p-wave superfluids Ammon, J.E., Kaminski, O Bannon

63 Fermionic excitations in holographic d-wave superfluids Fermi arcs Benini, Herzog, Yarom 2010 T = 0.59T c T = 0.49T c Density plot of Fermion spectral function 33

64 Summary An example of gauge/gravity duality applied to phase transitions in strongly coupled theories at finite temperature and density Meson melting At finite isospin density: ρ meson condensation Superfluidity: Frictionless motion of mesons Fermionic excitations Quantum phase transitions 34

65 (Selection of) Current activities and new results in gauge/gravity duality

66 (Selection of) Current activities and new results in gauge/gravity duality 1. Time-dependent processes, thermalization Romatschke; Chesler+Yaffe,...

67 (Selection of) Current activities and new results in gauge/gravity duality 1. Time-dependent processes, thermalization Romatschke; Chesler+Yaffe, Axial anomaly and hydrodynamics at finite baryon density J.E., Haack, Kaminski, Yarom; Loganayagam et al Chiral phase separation in rotating relativistic fluids Chiral magnetic effect in gauge/gravity duality Son, Surowka Landsteiner, Rebhan et al, Yee et al

68 (Selection of) Current activities and new results in gauge/gravity duality 1. Time-dependent processes, thermalization Romatschke; Chesler+Yaffe, Axial anomaly and hydrodynamics at finite baryon density J.E., Haack, Kaminski, Yarom; Loganayagam et al Chiral phase separation in rotating relativistic fluids Chiral magnetic effect in gauge/gravity duality Son, Surowka Landsteiner, Rebhan et al, Yee et al 3. Gauge/gravity duality at finite baryon density ( FAIR at GSI)

69 (Selection of) Current activities and new results in gauge/gravity duality 1. Time-dependent processes, thermalization Romatschke; Chesler+Yaffe, Axial anomaly and hydrodynamics at finite baryon density J.E., Haack, Kaminski, Yarom; Loganayagam et al Chiral phase separation in rotating relativistic fluids Chiral magnetic effect in gauge/gravity duality Son, Surowka Landsteiner, Rebhan et al, Yee et al 3. Gauge/gravity duality at finite baryon density ( FAIR at GSI) 4. Fermions Schalm, Zaanen et al; Liu, McGreevy et al

70 (Selection of) Current activities and new results in gauge/gravity duality 1. Time-dependent processes, thermalization Romatschke; Chesler+Yaffe, Axial anomaly and hydrodynamics at finite baryon density J.E., Haack, Kaminski, Yarom; Loganayagam et al Chiral phase separation in rotating relativistic fluids Chiral magnetic effect in gauge/gravity duality Son, Surowka Landsteiner, Rebhan et al, Yee et al 3. Gauge/gravity duality at finite baryon density ( FAIR at GSI) 4. Fermions Schalm, Zaanen et al; Liu, McGreevy et al 5. Quantum phase transitions Horowitz et al,... 35

71 Thanks to the Gauge/Gravity Duality group at MPI for Physics, Munich Postdocs: Dr. Andy O Bannon Dr. Shu Lin Dr. Veselin Filev PhD students: Viviane Grass Hai Thanh Ngo Patrick Kerner Constantin Greubel Steffen Müller Sebastian Halter Matthias Kaminski (now Princeton) Martin Ammon (now UCLA) Diplom/Master students: Saeid Aminian Jegors Korovins Hans-Jörg Zeller 36