Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30,...

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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

Transcript of Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30,...

Page 1: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Thermal Mass and Plasminofor Strongly Interacting Fermions via Holography

Yunseok Seo

Hanyang University

July 30, 2013

Based on arXiv:1205.3377 and arXiv:1305.1446in collaboration with Sang-Jin Sin and Yang Zhou

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

Page 2: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

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 + γip

i)/∆− ,

∆± = ω ∓ p−m2f

4p

[(1∓

ω

p

)log

(ω + p

ω − p

)± 2

]

Effective mass is generated by thermal and medium effect

m2f =

1

4g2(T

2+ µ

2π2)

Solving the pole of the propagator we will get two branches of dispersion

curves ω = ω±(p)

p << mf : ω±(p) ' mf ±1

3p

p >> mf : ω±(p) ' p

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

Page 3: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

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 + γip

i)/∆− ,

∆± = ω ∓ p−m2f

4p

[(1∓

ω

p

)log

(ω + p

ω − p

)± 2

]

Effective mass is generated by thermal and medium effect

m2f =

1

4g2(T

2+ µ

2π2)

Solving the pole of the propagator we will get two branches of dispersion

curves ω = ω±(p)

p << mf : ω±(p) ' mf ±1

3p

p >> mf : ω±(p) ' p

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

Page 4: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

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

mF

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

Page 5: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

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

mF

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

Page 6: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Down ApproachHolographic Setup

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

0 1 2 3 4 5 6 7 8 9

D4 • • • • •

D8, D8 • • • • • • • • •

Background geometry

Deconfined phase

ds2

=

(U

R

)3/2 (−f(U)dt

2+ d~x

2+ dx

24

)+

(R

U

)3/2(dU2

f(U)+ U

2dΩ

24

)

Confined phase

ds2

=

(U

R

)3/2 (ηµνdx

µdxν

+ f(U)dx24

)+

(R

U

)3/2(dU2

f(U)+ U

2dΩ

24

)

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

Page 7: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Down ApproachHolographic Setup

D brane embedding

Confined Phase

x4

r0

D8

D8

r

D4

m5 = SDBID4

Deonfined Phase

x4

rH

D8

D8

r

F1

m5 = 0

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

Page 8: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Dow ApproachFermion Green’s Function

Turn on fermionic fluctuation on probe brane

S =

∫d5x√−g

(ψΓM iDMψ −m5ψψ

)

DM = ∂M +1

4ωabMΓ

ab − iqAM

Equation of motion H. Liu et al.

(∂r +m5√grrσ

3)Φα =√grr/gii(iσ

2v(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)

)G2α

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

Page 9: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Down ApproachFermion Green’s Function

IR boundary condition can be determined by requiring regularity of equation

of motion at horizon (deconfined phase) or at the tip(confined phase)

Deconfined phase

G1,2(r0) = i

Confined phase

Gα(r0) =−mR+

√m2R2 + k2 − ω2

(−1)αk − ω

ω = ω +m5, m = m5r3/40

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

Page 10: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Down ApproachDispersion Relation: Confined Phase

Finite baryon mass

IR boundary condition

Gα(r0) =−m+

√m2 + k2 − ω2

(−1)αk − ω.

Continuum region

ω >√k2 +m2, ω < −

√k2 +m2

µ = 0

G1R

G2R

Continuum

Continuum mq = 0.1Μ0 = 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

Page 11: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Down ApproachDispersion Relation: Confined Phase

Finite baryon mass

µ 6= 0

Μ0=0.5Μ0=0.9Μ0=1.2Μ0=1.5Μ0=1.9Μ0=2.2

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

kΩ`

G1(k) = G2(−k)

Dispersion relations

Continuum

Continuum Μ0=0.6

-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 Μ0=1.5

-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 Μ0=2.0

-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

Page 12: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Down ApproachDispersion Relation: Confined Phase

Complex structure of pole in continuum region

A

B

C

0 < k < 0.4

Μ0=1.9

-0.4 -0.3 -0.2 -0.1 0.0-3

-2

-1

0

1

Re@Ω` D

Im@Ω`

D

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

Page 13: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Down ApproachDispersion 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√

6gT in weak coupling,

mT = 0 in strong coupling

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

Page 14: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Top Down ApproachDispersion Relation: Deonfined Phase

Deconfined phase

m5 = 0, µ 6= 0

m5 6= 0, µ 6= 0

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

Page 15: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Bottom Up ApproachSet up: Confined phase

Action

S =

∫dd+1x

√−g(R− 2Λ

16πGN−

1

4e2F 2 + i(ψΓMDMψ −mψψ)

)

We fix background geometry

Fermions coupled with gauge field

Equation of motion

Geometry: AdS soliton geometry in 5 dimension

ds2

= r2(−dt2 + d~x

2+ f(r)dx3) +

1

f(r)r2dr

2, f(r) := 1−

r40r4

Equation of motion for fermion

(∂r +m

r√fσ3)Φα =

1

r2√f

(iσ2(ω + eAt) + (−1)

αkσ

1)Φα

Equation of motion for gauge field

(√−ggttgrrφ′(r))′ −

√−ggtt〈ψ†ψ〉 = 0

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

Page 16: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Bottom Up ApproachSet up: Confined phase

Lutinger theorem

< ψψ† >=∑l

∫d2k

(2π)2Φ†lk(r)Φlk(r)θ(−ωl(k))

Equation of motion

(√−ggttgrrφ′(r))′ − e2

√gtt

grr

∑l

∫d2k

(2π)2Φ†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

Page 17: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Bottom Up ApproachDispersion 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

Page 18: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Bottom Up ApproachDeonfined 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

Page 19: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

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

Page 20: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

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

Page 21: Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30, 2013 Based on arXiv:1205.3377 and arXiv:1305.1446 in collaboration with Sang-Jin

Conclusion and Discussion

Thank you !!!

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