Thermal Mass and Plasmino for Strongly Interacting Fermions via - - PowerPoint PPT Presentation

Thermal Mass and Plasmino for Strongly Interacting Fermions via Holography

Yunseok Seo

Hanyang University

July 30, 2013

Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin Sin and Yang Zhou Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Motivation

Hard Thermal Loop(HTL) approximation in QCD

Fermion propagator G(p) = 1 γ · p − m − Σ(p) In the limit of m ≪ T, µ G = 1 2 (γ0 − γipi)/∆+ + 1 2 (γ0 + γipi)/∆− , ∆± = ω ∓ p − m2

f

4p

• 1 ∓ ω

p

• log

ω + p ω − p

• ± 2
• Yunseok Seo

Gague/Gravity Duality, Max Planck Institute for physics

Motivation

Hard Thermal Loop(HTL) approximation in QCD

Fermion propagator G(p) = 1 γ · p − m − Σ(p) In the limit of m ≪ T, µ G = 1 2 (γ0 − γipi)/∆+ + 1 2 (γ0 + γipi)/∆− , ∆± = ω ∓ p − m2

f

4p

• 1 ∓ ω

p

• log

ω + p ω − p

• ± 2
• Effective mass is generated by thermal and medium effect

m2

f = 1

4 g2(T 2 + µ2π2) Solving the pole of the propagator we will get two branches of dispersion curves ω = ω±(p) p << mf : ω±(p) ≃ mf ± 1 3 p p >> mf : ω±(p) ≃ p

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Motivation

Plasmino

Ω Ω

0.0 0.5 1.0 1.5 2.0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

p

2 ΩmF

Opposite direction with helicity and chirality Negative slope near zero momentum region (-1/3) Minimum at finite momentum Propagating anti-quark-hole in the medium

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Motivation

Plasmino

Ω Ω

0.0 0.5 1.0 1.5 2.0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

p

2 ΩmF

Opposite direction with helicity and chirality Negative slope near zero momentum region (-1/3) Minimum at finite momentum Propagating anti-quark-hole in the medium

Motivation

From direct solving Schwinger-Dyson equation, thermal mass seems to disappear at strong coupling limit arXiv:1111.0117, Nakkagawa et. al. The behavior of plasmino in strong coupling limit with finite temperature or finite density is not known in field theory We want to study thermal mass and plasmino in strong coupling by using AdS/CFT correspondence

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach

Holographic Setup

D4 brane background with D8, ¯ D8 brane as probe(Sakai & Sugimoto)

1 2 3 4 5 6 7 8 9 D4

• D8,

¯ D8

• Background geometry

Deconfined phase ds2 = U R 3/2 −f(U)dt2 + d x2 + dx2

4

• +

R U 3/2 dU 2 f(U) + U 2dΩ2

4

• Confined phase

ds2 = U R 3/2 ηµνdxµdxν + f(U)dx2

4

• +

R U 3/2 dU 2 f(U) + U 2dΩ2

4

• Turn on U(1) gauge field on the probe brane → Finite chemical potential

Fundamental strings in deconfined phase D4 baryon vertices in confined phase

Chemical potential µ = m5/q + ∞

r0

a′

0dr.

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach

Holographic Setup

D brane embedding

Confined Phase

x4

r0

D8 D8 r D4

m5 = SDBI

D4

Deonfined Phase

x4

rH

D8 D8 r

F1 m5 = 0

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Dow Approach

Fermion Green’s Function

Turn on fermionic fluctuation on probe brane S =

• d5x√−g
• ¯

ψΓMiDMψ − m5 ¯ ψψ

• DM = ∂M + 1

4 ωabMΓab − iqAM

Equation of motion H. Liu et al. (∂r + m5 √grrσ3)Φα =

• grr/gii(iσ2v(r) + (−1)αkσ1)Φα

v(r) =

• −gii/gtt(ω + qa0),

Φ1 = (y1, z1)T , Φ2 = (y2, z2)T

Retarded Green’s function

G1(r) := y1(r)/z1(r), G2(r) := y2(r)/z2(r)

gii grr ∂rGα + 2m5 √giiGα = (−1)αk + v(r) +

• (−1)α−1k + v(r)
• G2

α

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach

Fermion Green’s Function

IR boundary condition can be determined by requiring regularity of equation

• f motion at horizon (deconfined phase) or at the tip(confined phase)

Deconfined phase G1,2(r0) = i Confined phase Gα(r0) = −mR + √ m2R2 + k2 − ˆ ω2 (−1)αk − ˆ ω

ˆ ω = ω + m5, m = m5r3/4

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach

Dispersion Relation: Confined Phase

Finite baryon mass

IR boundary condition Gα(r0) = −m + √ m2 + k2 − ˆ ω2 (−1)αk − ˆ ω . Continuum region ˆ ω >

• k2 + m2,

ˆ ω < −

• k2 + m2

µ = 0

G1

R

G2

R

Continuum Continuum

mq 0.1 Μ0 0

0.0 0.2 0.4 0.6 0.8 1.0 1.0 0.5 0.0 0.5 1.0

k Ω

• Yunseok Seo

Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach

Dispersion Relation: Confined Phase

Finite baryon mass

µ = 0

Μ00.5 Μ00.9 Μ01.2 Μ01.5 Μ01.9 Μ02.2

Continuum Continuum

1.5 1.0 0.5 0.0 0.5 1.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5

k Ω

• G1(k) = G2(−k)

Dispersion relations

Continuum Continuum Μ00.6

1.5 1.0 0.5 0.0 0.5 1.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5

k Ω

• Continuum

Continuum Μ01.5

1.5 1.0 0.5 0.0 0.5 1.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5

k Ω

• Continuum

Continuum Μ02.0

1.5 1.0 0.5 0.0 0.5 1.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5

k Ω

• Yunseok Seo

Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach

Dispersion Relation: Confined Phase

Complex structure of pole in continuum region

A B C

0 k 0.4 Μ01.9

0.4 0.3 0.2 0.1 0.0 3 2 1 1

ReΩ ImΩ

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach

Dispersion Relation: Deonfined Phase

Deconfined phase

m5 = 0 IR boundary condition(Infalling condition) G1,2(r0) = i Result with µ = 0 No thermal mass generated mT = 1 √ 6 gT in weak coupling, mT = in strong coupling

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach

Dispersion Relation: Deonfined Phase

Deconfined phase

m5 = 0, µ = 0 m5 = 0, µ = 0

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Bottom Up Approach

Set up: Confined phase

Action S =

• dd+1x√−g

R − 2Λ 16πGN − 1 4e2 F 2 + i( ¯ ψΓMDMψ − m ¯ ψψ)

• We fix background geometry

Fermions coupled with gauge field

Equation of motion

Geometry: AdS soliton geometry in 5 dimension ds2 = r2(−dt2 + d x2 + f(r)dx3) + 1 f(r)r2 dr2 , f(r) := 1 − r4 r4 Equation of motion for fermion (∂r + m r√f σ3)Φα = 1 r2√f (iσ2(ω + eAt) + (−1)αkσ1)Φα Equation of motion for gauge field (

• −ggttgrrφ′(r))′ −
• −ggttψ†ψ = 0

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Bottom Up Approach

Set up: Confined phase

Lutinger theorem < ψψ† >=

• l
• d2k

(2π)2 Φ†

lk(r)Φlk(r)θ(−ωl(k))

Equation of motion (√−ggttgrrφ′(r))′ − e2

• gtt

grr

• l
• d2k

(2π)2 Φ†

lk(r)Φlk(r)θ(−ωl(k)) = 0

Solve coupled equation of motion by using iteration method

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Bottom Up Approach

Dispersion relation: Confined phase

IR boundary condition Gα(r0) = −mR + √ m2R2 + k2 − ω2 (−1)αk − ω Dispersion relation

0.0 0.5 1.0 1.5 2.0 0.0 0.2 0.4 0.6 0.8

k

Ω

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Bottom Up Approach

Deonfined phase

In deconfined phase, all dynamical fermions fall into the black hole Background becomes RN-AdS black hole We put probe fermion in the bulk Spectral density

Herzog et. al Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Summary

The condition for existence of plasmino mode Top down Bottom up Confining Deconfining Confining Deconfining mq = 0 > 0 ⊚ ⊚ µ < µc > µc ⊚ ⊚ ⊚ ⊚ Rashiba effect in bulk H± = k2 2meff(r) + αE(r) × σ · k + . . . ,

The field theory dual of spin-orbit coupling in bulk can be a density generated plasmino ω± ∼ αk2 ± βµ · k − µ

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Conclusion and Discussion

We calculate fermion Green’s function by using AdS/CFT correspondence In deconfined phase, there is no thermal mass generation In confined phase, plasmino excitations are present in certain window of chemical potential We speculate that the spin-orbit coupling in bulk is dual of plasmino mode in boundary theory

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Conclusion and Discussion

Thank you !!!

Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics