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 1 G ( p ) = γ · p − m − Σ( p ) In the limit of m ≪ T, µ 1 2 ( γ 0 − γ i p i ) / ∆ + + 1 2 ( γ 0 + γ i p i ) / ∆ − , G = � ω + p m 2 �� 1 ∓ ω � � � f ∆ ± = ω ∓ p − log ± 2 4 p p ω − p Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Motivation Hard Thermal Loop(HTL) approximation in QCD Fermion propagator 1 G ( p ) = γ · p − m − Σ( p ) In the limit of m ≪ T, µ 1 2 ( γ 0 − γ i p i ) / ∆ + + 1 2 ( γ 0 + γ i p i ) / ∆ − , G = � ω + p m 2 �� 1 ∓ ω � � � f ∆ ± = ω ∓ p − log ± 2 4 p p ω − p Effective mass is generated by thermal and medium effect f = 1 4 g 2 ( T 2 + µ 2 π 2 ) m 2 Solving the pole of the propagator we will get two branches of dispersion curves ω = ω ± ( p ) ω ± ( p ) ≃ m f ± 1 p << m f : 3 p p >> m f : ω ± ( p ) ≃ p Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Motivation Plasmino 2.0 1.8 1.6 2 Ω � m F Ω � 1.4 1.2 Ω � 1.0 0.8 0.6 0.0 0.5 1.0 1.5 2.0 p 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 2.0 1.8 1.6 2 Ω � m F Ω � 1.4 1.2 Ω � 1.0 0.8 0.6 0.0 0.5 1.0 1.5 2.0 p 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, D 8 brane as probe(Sakai & Sugimoto) 0 1 2 3 4 5 6 7 8 9 D4 • • • • • ¯ D8, D 8 • • • • • • • • • Background geometry Deconfined phase � U � R � 3 / 2 � dU 2 � � 3 / 2 � ds 2 = − f ( U ) dt 2 + d� x 2 + dx 2 � f ( U ) + U 2 d Ω 2 + 4 4 R U Confined phase � U � R � 3 / 2 � � � 3 / 2 � dU 2 ds 2 = η µν dx µ dx ν + f ( U ) dx 2 � f ( U ) + U 2 d Ω 2 + 4 4 R U 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 � ∞ a ′ µ = m 5 /q + 0 dr. r 0 Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach Holographic Setup D brane embedding Confined Phase D4 D8 x4 D8 r r0 m 5 = S DBI D 4 Deonfined Phase D8 x4 D8 F1 r rH m 5 = 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 � d 5 x √− g � � ψ Γ M iD M ψ − m 5 ¯ ¯ S = ψψ D M = ∂ M + 1 4 ω abM Γ ab − iqA M Equation of motion H. Liu et al. √ g rr σ 3 )Φ α = � g rr /g ii ( iσ 2 v ( r ) + ( − 1) α kσ 1 )Φ α ( ∂ r + m 5 � Φ 1 = ( y 1 , z 1 ) T , Φ 2 = ( y 2 , z 2 ) T v ( r ) = − g ii /g tt ( ω + qa 0 ) , Retarded Green’s function G 1 ( r ) := y 1 ( r ) /z 1 ( r ) , G 2 ( r ) := y 2 ( r ) /z 2 ( r ) � g ii √ g ii G α = ( − 1) α k + v ( r ) + ( − 1) α − 1 k + v ( r ) G 2 � � ∂ r G α + 2 m 5 α g rr 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 of motion at horizon (deconfined phase) or at the tip(confined phase) Deconfined phase G 1 , 2 ( r 0 ) = i Confined phase √ m 2 R 2 + k 2 − ˆ G α ( r 0 ) = − mR + ω 2 ( − 1) α k − ˆ ω m = m 5 r 3 / 4 ω = ω + m 5 , ˆ 0 Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach Dispersion Relation: Confined Phase Finite baryon mass IR boundary condition √ m 2 + k 2 − ˆ G α ( r 0 ) = − m + ω 2 . ( − 1) α k − ˆ ω Continuum region � k 2 + m 2 , � k 2 + m 2 ω > ˆ ω < − ˆ µ = 0 1.0 Continuum 0.5 R G 2 Ω � 0.0 R G 1 � 0.5 Continuum m q � 0.1 Μ 0 � 0 � 1.0 0.0 0.2 0.4 0.6 0.8 1.0 k Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach Dispersion Relation: Confined Phase Finite baryon mass µ � = 0 1.5 Continuum 1.0 0.5 Ω � 0.0 Μ 0 � 0.5 Μ 0 � 0.9 Μ 0 � 1.2 Μ 0 � 1.5 � 0.5 Μ 0 � 1.9 Continuum Μ 0 � 2.2 � 1.0 � 1.5 � 1.0 � 0.5 0.0 0.5 1.0 1.5 k G 1 ( k ) = G 2 ( − k ) Dispersion relations 1.5 1.5 1.5 Continuum Continuum Continuum 1.0 1.0 1.0 0.5 0.5 0.5 Ω Ω Ω � � � 0.0 0.0 0.0 � 0.5 � 0.5 � 0.5 Continuum Μ 0 � 0.6 Continuum Μ 0 � 1.5 Continuum Μ 0 � 2.0 � 1.0 � 1.0 � 1.0 � 1.5 � 1.0 � 0.5 0.0 0.5 1.0 1.5 � 1.5 � 1.0 � 0.5 0.0 0.5 1.0 1.5 � 1.5 � 1.0 � 0.5 0.0 0.5 1.0 1.5 k k k Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach Dispersion Relation: Confined Phase Complex structure of pole in continuum region 1 C A 0 � � Im � Ω B � 1 � 2 0 � k � 0.4 Μ 0 � 1.9 � 3 � 0.4 � 0.3 � 0.2 � 0.1 0.0 � � Re � Ω Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach Dispersion Relation: Deonfined Phase Deconfined phase m 5 = 0 IR boundary condition(Infalling condition) G 1 , 2 ( r 0 ) = i Result with µ = 0 No thermal mass generated 1 m T = √ gT in weak coupling , 6 m T = 0 in strong coupling Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Top Down Approach Dispersion Relation: Deonfined Phase Deconfined phase m 5 = 0, µ � = 0 m 5 � = 0, µ � = 0 Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Bottom Up Approach Set up: Confined phase Action � R − 2Λ 1 � � d d +1 x √− g 4 e 2 F 2 + i ( ¯ ψ Γ M D M ψ − m ¯ S = ψψ ) − 16 πG N We fix background geometry Fermions coupled with gauge field Equation of motion Geometry: AdS soliton geometry in 5 dimension f ( r ) := 1 − r 4 1 ds 2 = r 2 ( − dt 2 + d� x 2 + f ( r ) dx 3 ) + f ( r ) r 2 dr 2 , 0 r 4 Equation of motion for fermion m 1 r √ f σ 3 )Φ α = r 2 √ f ( iσ 2 ( ω + eA t ) + ( − 1) α kσ 1 )Φ α ( ∂ r + Equation of motion for gauge field − gg tt g rr φ ′ ( r )) ′ − − gg tt � ψ † ψ � = 0 � � ( Yunseok Seo Gague/Gravity Duality, Max Planck Institute for physics

Bottom Up Approach Set up: Confined phase Lutinger theorem d 2 k � < ψψ † > = (2 π ) 2 Φ † � lk ( r )Φ lk ( r ) θ ( − ω l ( k )) l Equation of motion � d 2 k g tt � ( √− gg tt g rr φ ′ ( r )) ′ − e 2 (2 π ) 2 Φ † � lk ( r )Φ lk ( r ) θ ( − ω l ( k )) = 0 g rr l 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 √ m 2 R 2 + k 2 − ω 2 G α ( r 0 ) = − mR + ( − 1) α k − ω Dispersion relation 0.8 0.6 0.4 Ω 0.2 0.0 0.0 0.5 1.0 1.5 2.0 k 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 = 0 m q > 0 ⊚ ⊚ < µ c µ > µ c ⊚ ⊚ ⊚ ⊚ Rashiba effect in bulk k 2 H ± = 2 m eff ( r ) + αE ( r ) × σ · k + . . . , The field theory dual of spin-orbit coupling in bulk can be a density generated plasmino ω ± ∼ αk 2 ± 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