Probes in holographic plasmas with unquenched quarks Liuba Mazzanti - PowerPoint PPT Presentation

Introduction D3/D7 plasma D7 probes End Probes in holographic plasmas with unquenched quarks Liuba Mazzanti (University of Santiago de Compostela) based on: A. Maga˜ na, J. M´ as, LM, J. Tarr´ ıo [arXiv:1205.xxxx] University of Crete, May 16, 2012 Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 1 / 29

Introduction D3/D7 plasma D7 probes End We start from: . . . Benini et al 06, Bigazzi et al 08, 09, 11 . . . (top-down) Mateos et al 06, 07 . . . , Erdmenger et al 06 . . . Quark-gluon plasma ⇔ Holographic plasma Finite temperature Black hole Unquenched quarks Smeared flavor branes Running coupling Dilaton profile Chemical potential Bulk gauge field r h ≃ 1 /πT T N f ∼ N c N f backreacted branes λ = 4 πg s N c e Φ( r ) λ = λ ( ε ) µ A t Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 2 / 29

Introduction D3/D7 plasma D7 probes End . . . and want to go: Casalderrey-Solana et al 11 ⇔ Quark-gluon plasma ? Holographic plasma Meson melting Quarkonia Quarkonia (+lattice) Screening length (SC) Conductivity Energy loss Drag force Diffusion constant Transv. mom. broad. J/ ψ spectrum dN/d 3 p c vs. M q V ¯ ” qq σ DC σ Nucl. mod. factor R π 0 M k and µ AA ” ˆ q Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 3 / 29

Introduction D3/D7 plasma D7 probes End Outline Review: D3/D7 plasmas D7 probes Constituent mass Quark condensate Conductivity at finite chemical potential Quark-antiquark potential Drag force for a moving heavy quark Kinetic mass Jet quenching parameter Conclusions Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 4 / 29

Introduction D3/D7 plasma D7 probes End D3 black hole Witten 98 r N c D3 at the tip of a Calabi-Yau cone X 5 with base X 5 (e.g. S 5 , T 1 , 1 ) D3 extend over R 1 , 3 at finite temperature T ↔ r h r h ⇓ near horizon Scwarzchild AdS 5 × X 5 D3 � 1,3   ds 2 = r 2 � − (1 − r 4 r 4 ) dt 2 + d� � KE + r 2 ( dτ + A KE ) 2 + R 2 dr 2 x 2 � + r 2 ds 2 h R 2 3 r 2  � r 4  1 − h r 4 Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 5 / 29

Introduction D3/D7 plasma D7 probes End Probe D7 in the D3 black hole Karch Katz 02 D7 r probe D7 wrapping X 3 ⊂ X 5 ( ξ, θ, φ ) r min D7 extends over R 1 , 3 and r quark mass M c : string stretching D3 � D7 from the D7 to the D3 r h ⇓ embedding τ = τ 0 , χ = χ ( r ) D3 � 1,3 χ ( r ) ≃ m r + c r 3 + . . . , r → ∞ Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 6 / 29

Introduction D3/D7 plasma D7 probes End Smeared D7 in the D3 black hole Benini Canoura Cremonesi Nu˜ nez Ramallo 07 . . . r N f smeared D7 along X 5 /X 3 ( χ ( r ) ) r min N f ∼ N c ≫ 1 smearing preserves N = 1 susy (broken) r min still determines the quark mass r h ⇓ smeared embedding form Ω 2 D3 � 1,3 N f � � � d 8 x − d 8 x Ω 2 → N f Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 7 / 29

Introduction D3/D7 plasma D7 probes End Backreacted D3/D7 black hole D7 r N f backreacted D7 smeared on X 5 r min running dilaton λ ( r ) = 4 πg s N c e Φ( r ) Landau pole in the far UV: r LP ≫ r h ⇓ r h backreaction expansion in ǫ h = Vol( X 3 ) N f λ h Vol( X 5 ) 16 π N c D3 � 1,3 � − 1 � G rr = R 2 � 1 − r 4 � � 1 + ǫ h 4 + O ( ǫ 2 � r + O ( ǫ 2 h ) , Φ = Φ h + ǫ h log h ) , r 2 r 4 r h h G KE = R 2 � 1 + ǫ h 12 + O ( ǫ 2 G ττ = R 2 � 1 − ǫ h 12 + O ( ǫ 2 � � h ) , h ) Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 8 / 29

Introduction D3/D7 plasma D7 probes End Scales in the D3/D7 plasma r r LP r h sets the temperature Landau Pole region r min = 0 for background ⇒ massless quarks effective and full theory coincide for r < r ∗ Landau Pole r LP ≈ r ∗ e 1 /ǫ h ≪ 1 r � effective theory boundary conditions at r ∗ : G, φ = G (0) , φ (0) validity validity of expansions: ǫ h | log r h r ∗ | ≪ 1 expansions validity our range: r h ≤ r ≪ r h e 1 /ǫ h r h � � h Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 9 / 29

Introduction D3/D7 plasma D7 probes End Flavored vs. unflavored background: temp and energy Unflavored Flavored r (0) r h = πTR 2 � 1 + ǫ h 8 + O ( ǫ 2 = πTR 2 � h ) h � � N (0) 2 ε 2 2 ε 2 � 1 − ǫ h 4 + O ( ǫ 2 � = N c = h ) c πT 2 3 3 πT 2 Comparison scheme Fixed observables: temperature T , energy density ε Varying parameters: horizon size r h , number of colors N c As the number of flavors N f ⇔ ǫ h varies � 2 ε � � πTR 2 − 1 r � � + O ( ǫ 2 ⇒ λ = 8 g s 1 + ǫ h log h ) 3 T 4 4 Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 10 / 29

Introduction D3/D7 plasma D7 probes End Parameters in the D3/D7 plasma r r LP LP realistic setup: r � coupling λ h ∼ 6 π number of colors N c ∼ 3 effective theory number of flavors N f ∼ 3 validity ⇓ perturbative parameter ǫ h ∼ 0 . 24 ⇓ expansions validity UV cutoff range r � 10 r h r min r h � � h Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 11 / 29

Introduction D3/D7 plasma D7 probes End Probe D7 embedding in the flavored background Maga˜ na M´ as LM Tarr´ ıo m D7 r probe D7 wrapping X 3 ⊂ X 5 ( ξ, θ, φ ) r min D7 extends over R 1 , 3 and r m as boundary condition at ∞ √ bare mass M q = 1 λ h T m 2 r h ⇓ embedding τ = τ 0 , ψ = sin χ ( r,ǫ h ) 2 D3 � 1,3 r 2 r 2 � � �� � ψ ( ∞ ) ≃ r h m 1 + m 0 log r h 6 c 0 log r h � c 1 + 5 + O ( ǫ 2 m 0 + c 0 r 2 + ǫ h h r + h r + . . . h ) r 2 r Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 12 / 29

Introduction D3/D7 plasma D7 probes End Flavored vs. unflavored embedding m Ρ cos Θ D7 Flavored r M c � 0 � r min Unflavored r min m r min r h Ρ sin Θ � 0 � r min r h Quark bare mass (dimension-less) m = m 0 + ǫ h m 1 + . . . D3 from holographic renormalization � 1,3 r 2 r 2 � � �� � ψ ( ∞ ) ≃ r h m 1 + m 0 log r h 6 c 0 log r h � c 1 + 5 + O ( ǫ 2 m 0 + c 0 r 2 + ǫ h h r + h r + . . . h ) r 2 r Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 13 / 29

Introduction D3/D7 plasma D7 probes End Flavored vs. unflavored background: mass Unflavored Flavored r (0) 1 + ǫ h = πTR 2 r h = πTR 2 � 8 + O ( ǫ 2 � h ) h � � N (0) 2 ε 2 2 ε 2 1 − ǫ h 4 + O ( ǫ 2 � � = N c = h ) c 3 πT 2 3 πT 2 r (0) min = r (0) r min = r (0) min ( m ) + ǫ h r (1) min ( m ) + O ( ǫ 2 min ( m ) h ) Comparison scheme Fixed observables: T , ε , rest mass m ≡ m 0 + ǫ h m 1 + . . . Varying parameters: r h , N c , UV cutoff r min As the number of flavors N f ⇔ ǫ h varies Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 14 / 29

Introduction D3/D7 plasma D7 probes End Constituent mass ր M c 1 Λ T 2 Flavored 6 Ε h � 0.25 4 Unflavored 2 M q m � 1 2 4 6 8 Λ T 2 2 √− G tt G rr � r min Φ 1 M c = dr e 2 πα ′ r h �� � 2 r min ( m ) log r min ( m ) 1 1 + 3 ǫ h ( r min ( m ) − r h ( T )) + ǫ h � � = λ h ( ε ) r h ( T ) + . . . 2 R 2 8 Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 15 / 29

Introduction D3/D7 plasma D7 probes End Minkowski vs. black-hole embedding Ρ cos Θ Ψ h Mink Mink r M c BH r min r min r h m Ρ sin Θ Mink: constituent mass M c ( m > m ∗ ) BH BH: no M c , m < m ∗ + δm ∗ r h both Mink and BH for m ∗ ≤ m ≤ m ∗ + δm ∗ ⇓ D3 � 1,3 renormalized DBI+CS D7 action onshell I ren Karch O’Bannon Skenderis 05, Albash Johnson 11 � � ∂m 0 � � � � ∂r min = − 1 ∂I ren 2 c 1 + 7 ∂r min + ǫ h ∂m 1 � λ h N c T 3 + O ( ǫ 2 ∂r min + O ( ǫ 2 2 c 0 + ǫ h 6 c 0 h ) h ) 8 Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 16 / 29

Introduction D3/D7 plasma D7 probes End Minkowski vs. black-hole embedding Ρ cos Θ Ψ h Mink Mink r M c BH r min r min r h m Ρ sin Θ Mink: constituent mass M c ( m > m ∗ ) BH BH: no M c , m < m ∗ + δm ∗ r h both Mink and BH for m ∗ ≤ m ≤ m ∗ + δm ∗ ⇓ D3 � 1,3 renormalized DBI+CS D7 action onshell I ren Karch O’Bannon Skenderis 05, Albash Johnson 11 � � � � � ∂m 0 � ∂I ren ∂ψ h = − 1 2 c 1 + 7 ∂ψ h + ǫ h ∂m 1 � λ h N c T 3 + O ( ǫ 2 ∂ψ h + O ( ǫ 2 2 c 0 + ǫ h 6 c 0 h ) h ) 8 Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 16 / 29

Introduction D3/D7 plasma D7 probes End Quark condensate ց (negative as in Albash et al 07, Erdmenger Meyer and Shock 07) ǫ h = 0 , 0 . 25 , 0 . 5 �ΨΨ� �ΨΨ� � � ∆ m � Unflavored 0.20 0.10 0.15 Unflavored 0.10 0.05 Flavored 0.05 Flavored M q M q m � m � 0.00 0.5 1.0 1.5 2.0 1 0.85 0.90 0.95 1.00 1 Λ T Λ T 2 2 � 0.05 √ λ h T ∂I ren � ¯ ψψ � = 1 ∂I ren ∂M q = 2 ∂ (( m 0 + ǫ h m 1 + ... ) = − 1 2 c 1 ( m ) + 7 � λ h ( ε ) N c ( ε ) T 3 � � � + O ( ǫ 2 � 2 c 0 ( m ) + ǫ h 6 c 0 ( m ) h ) 8 Liuba Mazzanti (USC) Probes in D3D7 plasma U. Crete, May 16, 2012 17 / 29