Holographic Flavor Transport Andy OBannon Max Planck Institute for - - PowerPoint PPT Presentation

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Holographic Flavor Transport Andy OBannon Max Planck Institute for - - PowerPoint PPT Presentation

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Holographic Flavor Transport Andy OBannon Max Planck Institute for Physics Munich, Germany 15th European Workshop on String Theory Zrich, Switzerland Credits 0705.3870 A. Karch and A. OB. 0708.1994 A. OB. 0808.1115 A.

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SLIDE 1

Holographic Flavor Transport

Andy O’Bannon Max Planck Institute for Physics Munich, Germany

15th European Workshop on String Theory Zürich, Switzerland

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SLIDE 2

Credits

  • 0705.3870 A. Karch and A. O’B.
  • 0708.1994 A. O’B.
  • 0808.1115 A. O’B.
  • 0812.3629 A. Karch, A. O’B., E. Thompson
  • 0908.2625 M. Ammon, H.T. Ngo, A. O’B.
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SLIDE 3

Outline:

  • I. Motivation
  • II. The System
  • III. The Conductivity
  • IV. Summary and Outlook
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SLIDE 4
  • I. Motivation

REAL Strongly-coupled Systems Strongly-coupled, Nearly-ideal FLUID Quantum Chromodynamics (QCD) Relativistic Heavy-Ion Collider (RHIC)

QCD at

T ≤ 2 × Tc

Tc ≈ 170 MeV

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SLIDE 5

Question: Can we compute TRANSPORT COEFFICIENTS for QCD at RHIC temperatures?

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SLIDE 6

Question: Can we compute TRANSPORT COEFFICIENTS for QCD at RHIC temperatures? Answer: NO.

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SLIDE 7

Philosophy: CHANGE the Question

Question: Can we find ANY STRONGLY-COUPLED system for which we CAN compute TRANSPORT COEFFICIENTS?

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SLIDE 8

Answer: YES!

N = 4 supersymmetric SU(Nc) Yang-Mills (SYM)

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SLIDE 9

Use Gauge-gravity Duality

Shear Viscosity

⎯

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SLIDE 10

GOAL

Compute a CONDUCTIVITY associated with “Quarks” or “Electrons” using Gauge-gravity Duality

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SLIDE 11

RESULT

Current nonlinear in E Pair Production Drude Conductivity

σ = N f

2Nc 2

16π 2 T 2 e2 +1f (m) + d 2 e2 +1

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SLIDE 12

Outline:

  • I. Motivation
  • II. The System
  • III. The Conductivity
  • IV. Summary and Outlook
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SLIDE 13

N = 4 supersymmetric SU(Nc) Yang-Mills (SYM)

  • II. The System

β = 0

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SLIDE 14

N = 4 supersymmetric SU(Nc) Yang-Mills (SYM)

  • II. The System

No Quarks!

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SLIDE 15

Nf N = 2 hypermultiplets

ADD fixed << “Probe Limit’’ β = +Ο N f Nc ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

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SLIDE 16

Scales

Temperature Mass Jμ Baryon Number Density symmetry current

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SLIDE 17

“Two-fluid” picture Electric Field

Lorentz force = Drag Force

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SLIDE 18

Translation Invariance Momentum Conservation

Steady-state???

Net Charge + Constant Electric Field Net Work

NO DISSIPATION!

⇒ ⇒

ENTIRE SYSTEM ACCELERATES FOREVER

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SLIDE 19

Probe Limit MIMICS Dissipation

∂µ T µν = Fνσ Jσ

∂t T tt = E Jx

∂t T tx = −E Jt

Jµ = Ο(N f Nc)

E = Ο(1)

Tµν = Ο(Nc

2)µν + Ο(N f Nc)µν

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SLIDE 20

N = 4 SYM

Supergravity

=

Nf N = 2 hypers. Nf probe D7-branes

=

Finite temperature

=

AdS-Schwarzschild

Holographic Dual

J µ

m

AdS5 × S3

= =

Embedding

Aµ

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SLIDE 21

The Method

  • NOT Kubo formula!
  • Compute 1-pt. function DIRECTLY
  • Exploit Born-Infeld dynamics with E field
  • Valid for any Dp/Dq system

SD7 = −N fTD7 d 8x −det(gab + (2πα ')F

ab)

∫

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SLIDE 22

Outline:

  • I. Motivation
  • II. The System
  • III. The Conductivity
  • IV. Summary and Outlook
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SLIDE 23
  • III. The Conductivity

d = J t π 2 λT 2

e = E π 2 λT 2

σ = N f

2Nc 2

16π 2 T 2 e2 +1f (m) + d 2 e2 +1

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SLIDE 24
  • III. The Conductivity

σ = N f

2Nc 2

16π 2 T 2 e2 +1f (m) + d 2 e2 +1

Depends on E!

J x = σ(E)E

Linearize in E

J x = σ(0)E

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SLIDE 25
  • III. The Conductivity

σ = N f

2Nc 2

16π 2 T 2 e2 +1f (m) + d 2 e2 +1

Pair Production

J t = 0

σ ≠ 0

BUT

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SLIDE 26
  • III. The Conductivity

σ = N f

2Nc 2

16π 2 T 2 e2 +1f (m) + d 2 e2 +1

f (m) → 0

f (m) → 1

m → ∞

m → 0

⇒ ⇒

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SLIDE 27
  • III. The Conductivity

σ = N f

2Nc 2

16π 2 T 2 e2 +1f (m) + d 2 e2 +1

T tx ∝ J t

NO momentum flow at zero density

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SLIDE 28
  • III. The Conductivity

σ = N f

2Nc 2

16π 2 T 2 e2 +1f (m) + d 2 e2 +1

Drude Conductivity Linearize in E σ(0)

m → ∞

Take

σ → d = J t π 2 λT 2

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SLIDE 29

dp dt = −µp + E

Why m → ∞ ?

Charges behave as semi-classical quasi-particles:

µm = π 2 λT 2

Separate calculation

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SLIDE 30

µm = π 2 λT 2

Drude Conductivity

σ → d = J t π 2 λT 2 = J t µm

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Outline:

  • I. Motivation
  • II. The System
  • III. The Conductivity
  • IV. Summary and Outlook
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  • IV. Summary + Outlook

Computed CONDUCTIVITY for a “DISSIPATIVE” STRONGLY-COUPLED Non-Abelian Gauge Theory Probe Branes are Great!

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FUTURE DIRECTIONS

MORE TRANSPORT COEFFICIENTS: Thermo-electric Transport

Condensed Matter Applications:

Superfluidity Non-relativistic Theories Magnetic Fields Anomalous currents Quantum Hall Effect

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SLIDE 34

Thank You.