Semi-holography for heavy-ion collisions Anton Rebhan with: Ayan Mukhopadhyay, Florian Preis & Stefan Stricker Institute for Theoretical Physics TU Wien, Vienna, Austria Oxford, May 17, 2016 A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 1 / 20
Semi-holographic models Semi-holography: dynamical boundary theory coupled to a strongly coupled conformal sector with gravity dual oxymoron coined by Faulkner & Polchinski, JHEP 1106 (2011) 012 [arXiv:1001.5049] in study of holographic non-Fermi-liquid models retains only the universal low energy properties, which are most likely to be relevant to the realistic systems allows more flexible model-building further developed for NFLs in: A. Mukhopadhyay, G. Policastro, PRL 111 (2013) 221602 [arXiv:1306.3941] A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 2 / 20
Semi-holographic model for heavy-ion collisions Aim: hybrid strong/weak coupling model of quark-gluon plasma formation (QCD: strongly coupled in IR, weakly coupled in UV) (different) successful example: J. Casalderrey-Solana et al., JHEP 1410 (2014) 19 and JHEP 1603 (2016) 053 Idea of semi-holographic model by E. Iancu, A. Mukhopadhyay, JHEP 1506 (2015) 003 [arXiv:1410.6448]: combine pQCD (Color-Glass-Condensate) description of initial stage of HIC through overoccupied gluons with AdS/CFT description of thermalization modified and extended recently in A. Mukhopadhyay, F. Preis, A.R., S. Stricker, arXiv:1512.06445 s.t. ∃ conserved local energy-momentum tensor for combined system verified in (too) simple test case A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 3 / 20
Gravity dual of heavy-ion collisions pioneered and developed in particular by P. Chesler & L. Yaffe [JHEP 1407 (2014) 086] most recent attempt towards quantitative analysis along these lines: Wilke van der Schee, Bj¨ orn Schenke, 1507.08195 had to scale down energy density by a factor of 20 (6) for the top LHC (RHIC) energies A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 4 / 20
Gravity dual of heavy-ion collisions pioneered and developed in particular by P. Chesler & L. Yaffe [JHEP 1407 (2014) 086] most recent attempt towards quantitative analysis along these lines: Wilke van der Schee, Bj¨ orn Schenke, 1507.08195 had to scale down energy density by a factor of 20 (6) for the top LHC (RHIC) energies perhaps improved by involving pQCD for (semi-)hard degrees of freedom? A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 4 / 20
pQCD and Color-Glass-Condensate framework recap: [e.g. F. Gelis et al., arXiv:1002.033] gluon distribution xG ( x, Q 2 ) in a proton rises very fast with decreasing longitudinal momentum fraction x at large, fixed Q 2 H1 and ZEUS xf xg 2 2 Q = 10 GeV 10 10 10 xS 1 1 1 xu v xd v -1 -1 -1 10 10 10 HERAPDF1.0 -2 -2 -2 exp. uncert. 10 10 10 model uncert. parametrization uncert. -3 -3 -3 10 10 10 -4 -3 -2 -1 10 10 10 10 1 x HIC: high gluon density ∼ α − 1 at “semi-hard” scale Q s ( ∼ few GeV) s weak coupling α s ( Q s ) ≪ 1 but highly nonlinear because of large occupation numbers description in terms of classical YM fields as long as gluon density nonperturbatively high A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 5 / 20
Color-Glass-Condensate evolution of HIC at LO effective degrees of freedom in this framework: color sources ρ at large x (frozen on the natural time scales of the strong 1 interactions and distributed randomly from event to event) gauge fields A µ at small x 2 (saturated gluons with large occupation numbers ∼ 1 /α s , with typical momenta peaked about k ⊥ Q s ) glasma: non-equilibrium matter, with high occupation numbers ∼ 1 /α s initially longitudinal chromo-electric and chromo-magnetic fields that are screened at distances 1 /Q s in the transverse plane of the collision A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 6 / 20
Color-Glass-Condensate evolution of HIC at LO colliding nuclei as shock waves with frozen color distribution t classical YM field equations D µ F µν ( x ) = δ ν + ρ (1) ( x − , x ⊥ ) + δ ν − ρ (2) ( x + , x ⊥ ) 3 in Schwinger gauge A τ = ( x + A − + x − A + ) /τ = 0 1 2 z with ρ from random distribution (varying event-by-event) 0 outside the forward light-cone (3): (causally disconnected from the collision) pure-gauge configurations A + = A − = 0 A i ( x ) = θ ( − x + ) θ ( x − ) A i (1) ( x ⊥ ) + θ ( − x − ) θ ( x + ) A i (2) ( x ⊥ ) A i (1 , 2) ( x ⊥ ) = i g U (1 , 2) ( x ⊥ ) ∂ i U † (1 , 2) ( x ⊥ ) � � � d x ∓ 1 ⊥ ρ (1 , 2) ( x ∓ , x ⊥ ) U (1 , 2) ( x ⊥ ) = P exp − i g ∇ 2 inside forward light-cone: numerical solution with initial conditions at τ = 0 : A i = A i A η = i g � � ∂ τ A i = ∂ τ A η = 0 (1) + A 1 A i (1) , A i (2) , , (2) 2 A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 7 / 20
Color-Glass-Condensate evolution of HIC at LO colliding nuclei as shock waves with frozen color distribution t classical YM field equations D µ F µν ( x ) = δ ν + ρ (1) ( x − , x ⊥ ) + δ ν − ρ (2) ( x + , x ⊥ ) 3 in Schwinger gauge A τ = ( x + A − + x − A + ) /τ = 0 1 2 z with ρ from random distribution (varying event-by-event) 0 outside the forward light-cone (3): (causally disconnected from the collision) pure-gauge configurations A + = A − = 0 A i ( x ) = θ ( − x + ) θ ( x − ) A i (1) ( x ⊥ ) + θ ( − x − ) θ ( x + ) A i (2) ( x ⊥ ) A i (1 , 2) ( x ⊥ ) = i g U (1 , 2) ( x ⊥ ) ∂ i U † (1 , 2) ( x ⊥ ) � � � d x ∓ 1 ⊥ ρ (1 , 2) ( x ∓ , x ⊥ ) U (1 , 2) ( x ⊥ ) = P exp − i g ∇ 2 inside forward light-cone: numerical solution with initial conditions at τ = 0 : A i = A i A η = i g � � ∂ τ A i = ∂ τ A η = 0 (1) + A 1 A i (1) , A i (2) , , (2) 2 Aim of semi-holographic model: include bottom-up thermalization from relatively soft gluons with higher α s and their backreaction when they build up thermal bath A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 7 / 20
Semi-holographic glasma evolution [E. Iancu, A. Mukhopadhyay, JHEP 1506 (2015) 003] [A. Mukhopadhyay, F. Preis, AR, S. Stricker, arXiv:1512.06445] UV-theory=classical Yang-Mills theory for overoccupied gluon modes with k ∼ Q s IR-CFT=effective theory of strongly coupled soft gluon modes k ≪ Q s , modelled by N=4 SYM gravity dual marginally deformed by: boundary metric g (b) µν , dilaton φ (b) , and axion χ (b) which are functions of A µ � � g (b) µν [ A ] , φ (b) [ A ] , χ (b) [ A ] S = S YM [ A ] + W CFT W CFT : generating functional of the IR-CFT (on-shell action of its gravity dual) minimalistic coupling through gauge-invariant dimension-4 operators = T µν coupled to δW CFT 2 √ 1 IR-CFT energy-momentum tensor δg (b) − g (b) µν energy-momentum tensor t µν of YM (glasma) fields through � 4 η µν F αβ F αβ � µν = η µν + γ t µν ( x ) = 1 − 1 g (b) α t µν , N c Tr F µα F ; ν Q 4 s � F µν � φ (b) = χ (b) = β F µν ˜ 4 N c Tr( F αβ F αβ ); 1 α 1 s h, h ( x ) = s a, a ( x ) = 4 N c Tr Q 4 Q 4 α, β, γ dimensionless and O (1 /N 2 c ) A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 8 / 20
Semi-holographic glasma evolution IR-CFT: marginally deformed AdS/CFT in Fefferman-Graham coordinates: α a ( x ) + · · · + z 4 4 πG 5 � z 6 � χ ( z, x ) = A ( x ) + O , Q 4 l 3 s β h ( x ) + · · · + z 4 4 πG 5 � z 6 � φ ( z, x ) = H ( x ) + O , Q 4 l 3 s l 2 G rr ( z, x ) = z 2 , G rµ ( z, x ) = 0 , l 2 + · · · + z 4 � 4 πG 5 � η µν + γ � G µν ( z, x ) = t µν ( x ) T µν ( x ) + P µν ( x ) z 2 Q 4 l 3 s � �� � � �� � 2 π 2 /N 2 g (b) c µν = g (0) µν �� z 4 ln z � + O , � 2 − Tr g 2 �� � with P µν = 1 + 1 2 ( g 2 (2) ) µν − 1 8 g (0) µν Tr g (2) 4 g (2) µν Tr g (2) (2) [de Haro, Solodukhin, Skenderis, CMP 217 (2001) 595] A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 9 / 20
Semi-holographic glasma evolution Modified YM (glasma) field equations � � δg (b) � αβ ( y ) δφ (b) ( y ) δχ (b) ( y ) δA µ ( x ) = δS YM δS δW CFT δA µ ( x ) + δW CFT δA µ ( x ) + δW CFT d 4 y δA µ ( x )+ δg (b) δφ (b) ( y ) δχ (b) ( y ) δA µ ( x ) αβ ( y ) gives � � D µ F µν = γ α − 1 + β � H F µν � + α � � T µα F ν ˆ α − ˆ T να F µ T α ˆ α F µν ˆ ∂ µ ˆ F µν ˜ D µ D µ A Q 4 2 Q 4 Q 4 s s s T αβ = δW CFT � − g ( b ) T αβ , H = δW CFT � A = δW CFT � with ˆ ˆ − g ( b ) H , ˆ − g ( b ) A = = = δg (b) δφ (b) δχ (b) αβ A. Rebhan Semi-holography for HIC Oxford, May 17, 2016 10 / 20
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