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 δn p ( t, x ) quasiparticles per unit momentum p Boltzmann equation: ∂δn p + v p · ∇ δn p + interactions = collisions ∂t 4

Zero sound in Fermi liquids δn p ( t, x ) quasiparticles per unit momentum p Boltzmann equation: ∂δn p + v p · ∇ δn p + interactions = collisions ∂t Low temperature: neglect collisions Solution: “zero sound” ω = ± vk − i Γ k 2 + O ( k 3 ) Non-isotropic deformation of Fermi surface 4

Properties of zero sound Speed v ≥ speed of sound v s 3.0 2.5 2.0 1.5 1.0 Zero sound 0.5 First sound 0.0 0 5 10 15 20 25 5

Properties of zero sound Speed v ≥ speed of sound v s π 2 T 2 + ω 2 Quasiparticle scattering rate: ν ∼ 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 � J t � • Compressible, d � J t � / d µ � = 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 � J t � • Compressible, d � J t � / d µ � = 0 Spectrum of collective excitations (quasinormal modes) includes low-temperature longitudinal modes with sound-like dispersion ω = ± vk − i Γ k 2 + O ( k 3 ) “Holographic zero sound” (HZS) Poles in two-point functions of T µν and J µ 8

HZS from probe branes Probe D q -branes with worldvolume ⊃ AdS p +1 factor [Karch, Son, Starinets, 0806.3796; Davison, Starinets, 1109.6343] Action � d p +2 ξ � S = S EH − T q − det( g + 2 πα ′ F ) Probe limit G N L 2 T q ≪ 1 – no back-reaction Non-zero electric field A 0 = A 0 ( z ) ⇒ chemical potential µ At T = 0 , QNMs √ p − ik 2 ω = ± k 2 pµ + O ( k 3 ) Pole in � JJ � correlators 9

HZS from probe branes Probe D q -branes with worldvolume ⊃ AdS p +1 factor [Karch, Son, Starinets, 0806.3796; Davison, Starinets, 1109.6343] Attenuation, e.g. p = 2 : - 7.5 - 8.0 - 8.5 - 9.0 - 9.5 - 10.0 - 10.5 - 11.0 - 8 - 7 - 6 - 5 - 4 - 3 10

⨯ ⨯ ■ ■ ■ ⨯ ■ ⨯ ⨯ ■ ■ ⨯ ⨯ ⨯ ⨯ ⨯ ■ ■ ■ HZS from probe branes Probe D q -branes with worldvolume ⊃ AdS p +1 factor [Karch, Son, Starinets, 0806.3796; Davison, Starinets, 1109.6343] T > 0 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] 1 � � R + d ( d − 1) � d d +1 x � − L 2 F 2 S = − det g 16 πG N L 2 AdS-Reissner-Nordstr¨ om solution: Non-zero electric field A 0 = A 0 ( z ) ⇒ chemical potential µ Low temperature pole in � JJ � and � TT � of form ω = ± vk − i Γ k 2 + O ( k 3 ) 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 - 11.6 - 11.8 ⨯ ⨯⨯⨯ ⨯⨯⨯ - 12.0 - 12.2 - 12.4 - 12.6 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 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] 0 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 AdS 2 ⇒ emergent scaling symmetry [Faulkner, Liu, McGreevy, Vegh, 0907.2694] Probe branes: • No evidence for Fermi surface • C ∼ T 2 p 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 AdS 2 ⇒ emergent scaling symmetry [Faulkner, Liu, McGreevy, Vegh, 0907.2694] Probe branes: • No evidence for Fermi surface • C ∼ T 2 p 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 1 � � R + d ( d − 1) � � d 4 x S = − det g L 2 16 πG N 0 � d 4 x � − T D − 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 1 � � R + d ( d − 1) � � d 4 x S = − det g L 2 16 πG N 0 � d 4 x � − T D − det( g + αF ) Admits charged black brane solutions: (2+1)-dimensional boundary CFT at T and µ Define 3 L 2 L 2 = 0 τ = 8 πG N L 2 T D , α = α/L 2 , ˜ 3 − 8 πG N T D L 2 0 τ ∼ N f /N c 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 0.0 - 0.2 - 0.4 - 0.6 - 0.8 - 1.0 - 1.0 - 0.5 0.0 0.5 1.0 20

τ = 10 − 4