Holographic zero sound from spacetime filling branes Ronnie Rodgers - - PowerPoint PPT Presentation

Holographic zero sound from spacetime filling branes

Ronnie Rodgers With Nikola Gushterov and Andy O’Bannon Based on arXiv:1807.11327

Outline

Background and motivation

• Fermi liquids
• Holographic zero sound

The model Results Summary and outlook

AdS/CMT

Gauge/gravity duality: Strongly coupled QFTs ⇔ Weakly coupled gravity theories Playground for strongly coupled physics without a quasiparticle description No quantitative predictions, but one can try to identify universal qualitative phenomena

2

Fermi liquids

System of fermions: adiabatically turn on repulsive interactions Landau theory: effective description of low-energy excitations in terms of quasiparticles Fermi liquids in nature:

• Helium-3
• Electron sea in metals

Useful reference point for understanding non-Fermi liquids (strange metals)

3

Zero sound in Fermi liquids

δnp(t, x) quasiparticles per unit momentum p Boltzmann equation: ∂δnp ∂t + vp · ∇δnp + interactions = collisions

4

Zero sound in Fermi liquids

δnp(t, x) quasiparticles per unit momentum p Boltzmann equation: ∂δnp ∂t + vp · ∇δnp + interactions = collisions Low temperature: neglect collisions Solution: “zero sound” ω = ±vk − iΓk2 + O(k3) Non-isotropic deformation of Fermi surface

4

Properties of zero sound

Speed v ≥ speed of sound vs

Zero sound First sound 5 10 15 20 25 0.0 0.5 1.0 1.5 2.0 2.5 3.0

5

Properties of zero sound

Speed v ≥ speed of sound vs Quasiparticle scattering rate: ν ∼ π2T 2 + ω2 µ(1 − e−ω/T ) Dial up temperature, attenuation:

• Quantum collisionless, T ≪ ω, Γ ∼ T 0
• Thermal collisionless, T 2/µ ≪ ω ≪ T, Γ ∼ T 2

Hydrodynamic sound, ω ≪ T 2/µ, Γ ∼ T −2 Zero sound → hydrodynamic sound as temperature increases

5

(Zero) sound attenuation

Maximum defines collisionless-to-hydrodynamic crossover

6

(Zero) sound attenuation

Zero sound attenuation in Helium-3 [Abel, Anderson, Wheatley, Phys. Rev. Lett. 17 (Jul, 1966) 74-78]

7

Holographic zero sound

Holographic models with bulk gauge field. Dual field theory:

• U(1) global symmetry
• Non-zero chemical potential µ, charge density Jt
• Compressible, dJt /dµ = 0

8

Holographic zero sound

Holographic models with bulk gauge field. Dual field theory:

• U(1) global symmetry
• Non-zero chemical potential µ, charge density Jt
• Compressible, dJt /dµ = 0

Spectrum of collective excitations (quasinormal modes) includes low-temperature longitudinal modes with sound-like dispersion ω = ±vk − iΓk2 + O(k3) “Holographic zero sound” (HZS) Poles in two-point functions of Tµν and Jµ

8

HZS from probe branes

Probe Dq-branes with worldvolume ⊃ AdSp+1 factor

[Karch, Son, Starinets, 0806.3796; Davison, Starinets, 1109.6343]

Action S = SEH − Tq

• dp+2ξ
• − det(g + 2πα′F)

Probe limit GNL2Tq ≪ 1 – no back-reaction Non-zero electric field A0 = A0(z) ⇒ chemical potential µ At T = 0, QNMs ω = ± k √p − ik2 2pµ + O(k3) Pole in JJ correlators

9

HZS from probe branes

Probe Dq-branes with worldvolume ⊃ AdSp+1 factor

[Karch, Son, Starinets, 0806.3796; Davison, Starinets, 1109.6343]

Attenuation, e.g. p = 2:

• 8
• 7
• 6
• 5
• 4
• 3
• 11.0
• 10.5
• 10.0
• 9.5
• 9.0
• 8.5
• 8.0
• 7.5

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HZS from probe branes

Probe Dq-branes with worldvolume ⊃ AdSp+1 factor

[Karch, Son, Starinets, 0806.3796; Davison, Starinets, 1109.6343]

T > 0 ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

■ ■ ■ ■ ■ ■ ■ ■ ■

Crossover to hydrodynamics when poles collide

11

HZS in Einstein-Maxell

U(1) gauge field minimally coupled to gravity

[Edalati, Jottar, Leigh, 1005.4075; Davison, Kaplis, 1111.0660]

S = 1 16πGN

• dd+1x
• − det g
• R + d(d − 1)

L2 − L2F 2

• AdS-Reissner-Nordstr¨
• m solution:

Non-zero electric field A0 = A0(z) ⇒ chemical potential µ Low temperature pole in JJ and TT of form ω = ±vk − iΓk2 + O(k3) Continuously becomes hydrodynamic sound at higher temperatures

12

HZS in Einstein-Maxell

U(1) gauge field minimally coupled to gravity

[Edalati, Jottar, Leigh, 1005.4075; Davison, Kaplis, 1111.0660]

Attenuation, d = 3

⨯ ⨯ ⨯⨯⨯ ⨯⨯⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

• 7
• 6
• 5
• 4
• 3
• 2
• 1
• 12.6
• 12.4
• 12.2
• 12.0
• 11.8
• 11.6

Small maximum – crossover?

13

HZS in Einstein-Maxell

U(1) gauge field minimally coupled to gravity

[Edalati, Jottar, Leigh, 1005.4075; Davison, Kaplis, 1111.0660]

⨯ ⨯

■

⨯ ⨯

No pole collision

14

What is the HZS mode?

These systems are not Fermi liquids:

Einstein-Maxwell models can have Fermi surface

[Liu, McGreevy, Vegh, 0903.2477; Cubrovic, Zaanen, Schalm, 0904.1993]

But at T = 0: near horizon AdS2 ⇒ emergent scaling symmetry

[Faulkner, Liu, McGreevy, Vegh, 0907.2694]

Probe branes:

• No evidence for Fermi surface
• C ∼ T 2p

No symmetry breaking ⇒ not (superfluid) phonon

15

What is the HZS mode?

These systems are not Fermi liquids:

Einstein-Maxwell models can have Fermi surface

[Liu, McGreevy, Vegh, 0903.2477; Cubrovic, Zaanen, Schalm, 0904.1993]

But at T = 0: near horizon AdS2 ⇒ emergent scaling symmetry

[Faulkner, Liu, McGreevy, Vegh, 0907.2694]

Probe branes:

• No evidence for Fermi surface
• C ∼ T 2p

No symmetry breaking ⇒ not (superfluid) phonon Properties of HZS show significant qualitative differences between the two models – why? What effective theories support zero sound?

15

Outline

Background and motivation

• Fermi liquids
• Holographic zero sound

The model Results Summary and outlook

Model

Spacetime filling brane with back-reaction S = 1 16πGN

• d4x
• − det g
• R + d(d − 1)

L2

• − TD
• d4x
• − det(g + αF)

Admits charged black brane solutions: (2+1)-dimensional boundary CFT at T and µ

17

Model

Spacetime filling brane with back-reaction S = 1 16πGN

• d4x
• − det g
• R + d(d − 1)

L2

• − TD
• d4x
• − det(g + αF)

Admits charged black brane solutions: (2+1)-dimensional boundary CFT at T and µ Define L2 = 3L2 3 − 8πGNTDL2 , τ = 8πGNL2TD, ˜ α = α/L2 τ ∼ Nf/Nc number of flavours in CFT ˜ α measures non-linearity of interaction Probe DBI and Einstein-Maxwell appear as limits

17

Plan

Study the collective excitations in this setup

• How does zero sound depend on parameters of the model?
• How do we recover previous regimes

For this talk: ˜ α = 1, vary τ We have also computed spectral functions

18

Outline

Background and motivation

• Fermi liquids
• Holographic zero sound

The model Results Summary and outlook

Motion of poles

τ = 0, ˜ α = 1, k/µ = 0.01

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯⨯ ⨯ ⨯

                                                                      ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

• 1.0
• 0.5

0.0 0.5 1.0

• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.0

⨯

 20

τ = 10−4

Motion of poles

τ = 10−4, ˜ α = 1, k/µ = 0.01

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

                                                                                

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

• 1.0
• 0.5

0.0 0.5 1.0

• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.0

22

τ = 10−3

Motion of poles

τ = 10−3, ˜ α = 1, k/µ = 0.01

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

                      ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

▲ ▲ ▲ ▲ ▲ ▲ ▲

• 1.0
• 0.5

0.0 0.5 1.0

• 2.0
• 1.5
• 1.0
• 0.5

0.0

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Motion of poles

τ = 10−3, ˜ α = 1, k/µ = 0.01

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

                                     

■ ■ ■ ■        

• 1.0
• 0.5

0.0 0.5 1.0

• 2.0
• 1.5
• 1.0
• 0.5

0.0

24

Motion of poles

τ = 10−3, ˜ α = 1, k/µ = 0.01

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

                                             

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

• 1.0
• 0.5

0.0 0.5 1.0

• 1.5
• 1.0
• 0.5

0.0

24

τ = 10−2

Motion of poles

τ = 10−2, ˜ α = 1, k/µ = 0.01

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

                                                        ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

* * * * * * * * * * * * * * * * * * * * * * * * * * * *

▲ ▲ ▲

• 4
• 2

2 4

• 10
• 8
• 6
• 4
• 2

26

Motion of poles

τ = 10−2, ˜ α = 1, k/µ = 0.01

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

■ ■ ■ ■ ■ ■ ■ ■ ■

▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲

• 1.0
• 0.5

0.0 0.5 1.0

• 10
• 8
• 6
• 4
• 2

Closest poles to real axis similar to Einstein-Maxwell

26

HZS attenuation

˜ α = 1, k/µ = 0.01

◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆

⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯⨯ ⨯ ⨯⨯⨯⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯ ⨯

                                                                     

+ + + + + +++++ ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

■ ■ ■ ■ ■ ■■■■■ ■ ■ ■ ■ ■■■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

* * * ** * ***** * **** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

▲▲▲▲▲ ▲ ▲▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲

• 8
• 6
• 4
• 2
• 12
• 11
• 10
• 9
• 8

◆

⨯



+

■ ▲

*

Reissner-Nordström AdS-Schwarzschild sound Probe zero sound

Qualitative resemblance to zero sound in Fermi liquids Temperature scaling quantitatively different (closer for small τ) Maximum shrinks with increasing back-reaction

27

Outline

Background and motivation

• Fermi liquids
• Holographic zero sound

The model Results Summary and outlook

Summary

Back-reacted spacetime filling branes exhibit a holographic zero sound mode This mode has qualitative similarities to zero sound in Fermi liquids The back-reaction parameter τ ∼ Nf/Nc appears to control the appropriate effective theory

29

Outlook

How generic is this mode?

• Is it universal in holographic models?
• If not, what controls its appearance? Non-zero

spectral weight at zero frequency?

• What does zero sound look like in holographic models
• f Fermi liquids?

Outside of holography, do low temperature sound modes exist in non-Fermi liquids?

30

Outlook

How generic is this mode?

• Is it universal in holographic models?
• If not, what controls its appearance? Non-zero

spectral weight at zero frequency?

• What does zero sound look like in holographic models
• f Fermi liquids?

Outside of holography, do low temperature sound modes exist in non-Fermi liquids?

Thank you!

30