Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30,...
Transcript of Thermal Mass and Plasmino for Strongly Interacting ... · Yunseok Seo Hanyang University July 30,...
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
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
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
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
2Ω
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
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
2Ω
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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