AdS/CFT and (some) Big Questions in Heavy Ion Collisions JORGE NORONHA. University of São Paulo

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1 AdS/CFT and (some) Big Questions in Heavy Ion Collisions JORGE NORONHA University of São Paulo 20 Years Later: The Many Faces of AdS/CFT, Princeton, Nov. 2017

2 Heavy Ion Collisions in a Nutshell QCD out of equilibrium Study deconfinement in the lab Quark-Gluon Plasma (QGP): the hottest, densest, smallest, most perfect (and vortical*) fluid ever made. *Nature 548, (2017) RHIC LHC 2

3 Some of the Big Questions in Heavy Ion Collisions - How do quarks and gluons conspire to form a strongly coupled nearly perfect liquid? - How do jets probe the inner workings of the QGP? - What is the role played by topological transitions in the QGP? RHIC What are the signatures of critical phenomena in QCD? RHIC BES 2019 Heavy Ions Holography In this talk I will show you how recent calculations in holography have changed our understanding about fluid dynamics 3

4 The ubiquitousness of fluid dynamics Based on conservations laws + large separation of length scales Separation of scales macroscopic: Knudsen number: microscopic: FLUID Macroscopic: Gradient of velocity field Example of microscopic scale (gas): ~1m ~ mean free path

5 Quark-Gluon Plasma: nature's first liquid Gale et al, PRL 110, (2013) There is large evidence that QGP is a strongly coupled relativistic liquid How does this emerge from QCD??? gluon self-interactions No explanation from first principles 5

6 Key input from holography: Universality of shear viscosity in QFT string theory in weakly curved backgrounds d.o.f. / vol. in QFT vanishing string coupling in QFT spatially isotropic black brane Corrections appear from anisotropy/inhomogeneities or higher order derivatives in the bulk action Universality of black hole horizons Kovtun,Son,Starinets, PRL 2005 Nearly perfect fluidity Right ballpark for the QGP! HOLOGRAPHY Universality of transport coefficient in QFT 6

7 Pushing the boundaries of fluid dynamics: Quark-Gluon Plasma From , it seemed that hydrodynamics was justified QGP was modeled as smooth fluid over scales of the order ~ 5-10 fm macro micro Knudsen number For such smooth distributions, it was natural to consider near equilibrium dynamics Fluid dynamics at scales of the size of a large nucleus 7

8 Hydrodynamics for relativistic strongly coupled fluids (e.g, conformal plasma) Flow velocity Inviscid part Dissipative part Landau frame Need + definition of Hydro as a gradient expansion: assumed to be small Key input from holography! BHMR, JHEP (2008) BRSSS, JHEP (2008) Power series in Knudsen number First order: Shear tensor Relativistic Navier-Stokes 8

9 To 2nd order in the expansion the famous fluid/gravity approach gives for a conformal fluid BHMR, JHEP (2008) - Fluid/gravity geometrization of the Chapman-Enskog expansion method for the Boltzmann equation. - Hydrodynamics systematic solution of Einstein's eqs. in the bulk - Good framework to study viscous fluids coupled to gravity. - Unearthed a series of new questions in physics and mathematics. 9

10 If we stop at 1st order relativistic Navier-Stokes: - Initial value problem requires in the initial spacelike hypersurface. - This theory is parabolic (Pichon, 1965): causality is an issue. - This theory is linearly unstable around equilibrium (Hiscock, Lindblom, 1984). On the other hand, the 2nd order theory - Initial value problem requires EOM are of 3rd order - Causality and well-posedness are tricky due to higher order derivatives (even if metric is flat) - A naive linearized analysis shows that this theory is acausal and unstable (though at large wavenumber) some resummation (e.g., Israel-Stewart) is needed 10

11 A mathematically consistent (though simplified) 2nd order theory See Bemfica, Disconzi, JN, arxiv: [gr-qc], Disconzi, arxiv: [math.ap] Inspired by fluid/gravity, one may consider Resummation of hydro fields For the solutions of coupled to Causality, existence, and uniqueness (full nonlinear level) + linear stability established for the first time. Extension of proof to full 2nd order is very challenging. 11

12 After 2010, the discovery of higher order harmonics of the QGP UNIVERSE QGP Figure from LRPNS 2015 has sparked a revolution in heavy ion collisions 12

13 Nowadays, the QGP is thought to be like this J. Noronha-Hostler, JN, M. Gyulassy, PRC 2016 Knudsen number QGP Schenke, Tribedy, Venugopalan, 2012 Hydrodynamic behavior at the scale of a proton??? No clear separation of scales macro microscopic scale??? LRPNS

14 Large order behavior of the gradient series and holography Heller, Janik, Witaszczyk, PRL 2013 : Large order behavior of the gradient expansion at strong coupling in N=4 SYM Rapidly expanding anisotropic fluid Bjorken flow Holography find (toy model QGP) Gradient series diverges! Energy density Impossible to find this at large order without holography 14

15 Large order behavior of the gradient series and holography - After nearly 90 years, we now know that the hydrodynamic gradient series has zero radius of convergence. - Same result found at weak coupling within kinetic theory G. Denicol and JN, arxiv: Optimal truncation at a given order can be compromised by causality and stability issues. What information is encoded in this divergence? Heller et al. 2013: After Borel resummation, leading pair of poles in the Borel plane were identified with the lowest non-hydrodynamic QNM's in the bulk. Was this a coincidence? Reminder: Ex: sound wave 15

16 Toy model for non-conformal QGP: N=2* gauge theory Pilch, Warner, Buchel, Peet, Polchinski, 2000 A relevant deformation of SYM: Breaking of SUSY N = 4 SYM theory + Bosonic mass Fermionic mass C. Hoyos, S. Paik, and L. G. Yaffe, JHEP 10, 062 (2011) 16

17 Holographic description N=2* classical gravity dual action: Pilch, Warner, Buchel, Peet, Polchinski, 2000 Scalar potential - Non-conformal strongly interacting plasma: Bulk viscosity compatible with QGP? - Used in tests of holography in non-conformal settings. A. Buchel, J. G. Russo, and K. Zarembo, N. Bobev, H. Elvang, D. Z. Freedman, and S. S. Pufu,

18 N=2* gauge theory in an expanding Universe Buchel, Heller, JN, arxiv: , PRD (2016) Expansion driven by another source of matter: no backreaction from holographic plasma Use characteristic formulation of gravitational dynamics in asymptoticaly AdS5 spacetimes Chesler,Yaffe, JHEP 2014 Assuming spatial isotropy and homogeneity leads to At boundary Encode non-equilibrium dynamics in a FRW Universe!!! 18

19 N=2* gauge theory in an expanding Universe Buchel, Heller, JN, arxiv: , PRD (2016) Conformal limit Analytical solution for SYM in FRW spacetime First studied by P. S. Apostolopoulos, G. Siopsis, and N. Tetradis, PRL (2009) Temperature Conformal anomaly: Energy density Pressure 19

20 Divergence of the gradient series at strong coupling Buchel, Heller, JN, arxiv: , PRD (2016) In the FRW case, the gradient expansion corresponds to Energy-momentum tensor equilibrium dissipation In terms of the energy density and pressure out-of-equilibrium (no shear due to symmetries) Bulk viscosity 20

21 Divergence of the gradient series at strong coupling Buchel, Heller, JN, arxiv: , PRD (2016) Entropy production Apparent horizon: For single component cosmologies Factorial growth Divergent series 21

22 Resummation of the gradient series at strong coupling FRW gives a clear and simple example where the hydrodynamic gradient expansion diverges. Divergence seems generic. FRW is simpler than Bjorken flow. Resummation of the series turns out to be simpler. Resummed entropy production: 22

23 Resummation of the gradient series at strong coupling Hydrodynamic (gradient) series Knudsen number Borel sum + Pade approximants Borel singularities = black brane non-hydro quasinormal modes Hydro series knows about whole high frequency completion 23

24 Resurgence theory and hydrodynamics Heller, Spalinski, Dunne, Basar, Aniceto, and etc ( ) Think of the Knudsen number coupling constant in a QFT Schematically, one may now write the problem as a trans-series Instanton terms given by the black brane non-hydrodynamic QNM's Systematic geometric realization via holography? Generalization of fluid/gravity correspondence? Non-locality in the bulk description? Universal behavior at late times? 24

25 Hydrodynamics as a non-equilibrium attractor Emergence of quasi-universal hydrodynamic behavior far from equilibrium See the review by Florkowski, Heller, and Spalinski, arxiv: Hydrodynamization See Wilke's talk! Bjorken flow Attractor N = 4 SYM From P. Romatschke, arxiv: [hep-th] 25

26 A partial list of the challenges one faces here - Real fluids have many Knudsen numbers (fields). Ex: Imagine trying to find leading terms in resurgent series in QFT with many couplings - Resummation machinery probably not as useful for realistic fluids without (a lot of) symmetry. QGP - First principles (e.g., holography, kinetic theory) derivation of the non-equilibrium attractor? - There should be a simple way to describe the attractor in the CFT - No idea how to construct it using holography (IR vs. UV issue). 26

27 Conclusion: Decade long synergy between QGP and holography PHASE 1 Motivated the understanding of near equilibrium properties of holographic fluids + holographic jet quenching ( ) RHIC Experiments Strongly coupled QGP PHASE 2 ( ) Highly inhomogeneous QGP Motivated the understanding of far-from-equilibrium holography (advent of numerical relativity) PHASE 3 ( ) Search for QCD critical point Holography as the only tool to investigate real time far-from-eq. dynamics + critical phenomena 27

28 EXTRA SLIDES 28

29 QCD Phase diagram Cartoon of the QCD diagram circa ~ 1980 Figure from G. Baym

30 Search for the QCD critical point (RHIC ) Current cartoon showing the different phases of QCD Crossover confirmed by lattice Critical point??? (same universality class as 3d Ising) Most of the phase diagram is not known due to the Fermi sign problem

31 The Fermi sign problem

32 Many-body systems at finite density: The Fermi sign problem In QCD, strongly correlated fermions in condensed matter, and etc Employ the Monte Carlo method: Sample using What if S is complex????

33 Many-body systems at finite density: The Fermi sign problem This problem appears in QCD at nonzero baryon chemical potential Even though is well defined Example: Many-body problem with exponential complexity Troyer, Wiese, PRL 94, (2005)

34 Consequences of the Fermi sign problem in QCD - Majority of QCD phase diagram: unknown - EOS of QCD matter in neutron stars unknown - Location of high T critical point: unknown RHIC Beam Energy Scan (BES) Major experimental effort (2019-) to search for the critical point using heavy ion collisions (STAR experiment)

35 QCD thermodynamics from a Taylor expansion Expand the QCD partition function in a Taylor series around Baryon susceptibilities Numerically very expensive Few coefficients are known Wuppertal Collab., JHEP (2012)

36 Doping the holographic QGP with quarks R. Rougemont, J. Noronha-Hostler, JN, PRL 2015 Bottom-up model by DeWolfe, Gubser, Rosen, Charged black hole baryon charge Predictions confirmed by latest lattice Taylor series results Lattice Pressure difference A. Bazavov et al. Phys. Rev. D 95 (2017) Baryon density 36

37 First realistic calculations of baryon susceptibilities Critelli, Noronha, Noronha-Hostler, Portillo, Ratti, Rougemont arxiv: Charged black hole 2 million numerical black hole solutions!! 37

38 Location of the QCD critical point from black hole physics Critelli, Noronha, Noronha-Hostler, Portillo, Ratti, Rougemont 2nd baryon susceptibility diverges at: CRITICAL POINT 38

39 Prediction from holographic modeling Critelli, Noronha, Noronha-Hostler, Portillo, Ratti, Rougemont Cumulants of the multiplicity of net protons Critical point: Fixed target experiments (FXT-RHIC, CBM-FAIR) This prediction can be verified at RHIC BES II: ( ) 39

40 Exclusion diagram for the location of the critical point Critelli, Noronha, Noronha-Hostler, Portillo, Ratti, Rougemont 40

41 Chemical freezeout parameters extracted from comparison to data STAR data PRL (2014) 41

42 Chemical freezeout parameters extracted from comparison to data 42

43 Numerical solution of Einstein's equations Black hole parameters Gauge theory 43

44 Universality class of QCD critical point QCD 3d Ising universality class 44

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47 First non-equilibrium calculations near a critical point Critelli, Rougemont, JN, arxiv: Real time calculations!! 47

48 Isotropization and thermalization near a critical point Critelli, Rougemont, JN, arxiv: Real time calculations!! Quasinormal modes 48

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52 Quark-Gluon Plasma (QGP): what we know from first principles QGP is a highly non-conformal strongly coupled non-abelian plasma Trace anomaly WB Coll., PLB (2014) HotQCD, PRD (2014) 52

53 QGP as nature's first liquid Equation of State of the early universe Borsanyi et al. Nature 539 (2016) QCD liquid QCD phase transition crossover Aoki et al. Nature 443 (2006) QCD out-of-equilibrium

54 Holographic black holes as viscosity calculators On-shell gravity action generator of retarded correlators Son, Starinets, 2002 Linearizing the action: Massless scalar field coupled to gravity in the bulk Retarded correlator in the gauge theory boundary Near equilibrium, linear response properties encoded in the horizon incoming wave at horizon Kubo formula horizon 54

55 Going beyond universality Bulk viscosity Bulk viscosity has been shown to be very relevant in heavy ion collisions. Ryu et al, PRL 2015 Bulk delays radial expansion Behavior of zeta is not universal Non-conformal holographic modeling is needed 55

56 Simplest phenomenological model for the non-conformal QGP Minimal holographic model for the non-conformal plasma Gubser, Nellore Gursoy et al, 2008 Phenomenology: Non-CFT behavior driven by an ad-hoc relevant scalar operator Scalar potential obtained from matching lattice data CFT Non CFT Dip in speed of sound 56

57 Black hole engineering and the non-conformal QGP Finazzo, Rougemont, Marrochio, JN, JHEP 2015, Critelli et al, PRD 2017 Combining most recent lattice data + numerical holography - Transport coefficients predictions of the model - Can simulate near-equilibrium and far-from-equilibrium behavior of the QGP Trace anomaly - Numerical relativity in asymptotic AdS Challenge: Only approach that is consistent with Bayesian analysis of heavy ion data Obtain such realistic behavior from string theory constructions 57

58 Connecting the BES scan to theory Fluctuations of net protons (STAR) Also net kaons and net charge Cumulants of eventby-event distributions Data / theory comparison

59 Current status from BES experimental data X. Luo (2016)?? Ratio of cumulants of net proton distributions Baryon number susceptibilities This quantity should be large near the critical point

60 Without the lattice guidance, alternative approaches must be used. Requirements for a reliable prediction: - Deconfinement - Nearly perfect fluidity - Agreement with lattice thermodynamics around crossover - Agreement with lattice results for baryon susceptibilities at zero baryon density THE WAY TO FULLFIL THESE CONDITIONS BLACK HOLES It is better to ask for forgiveness than permission

61 Doping the holographic QGP with quarks A high priority of nuclear science research in the US QCD Critical Point?? Perfect fluidity in a baryon-rich QGP??? Fig. from Long Range Plan Nuclear Science 2015 QCD Phase Diagram RHIC BES II ? 61

62 Why is hydrodynamics applicable in heavy ion collisions? Conventional wisdom: hydrodynamics as an effective theory Hydrodynamic behavior emerges when there is a large separation between macroscopic and microscopic scales J. Noronha-Hostler, JN, M. Gyulassy, PRC

63 What about weak coupling QCD? Sufficiently large T + asympt. freedom = QGP is a gas Not a perfect fluid!!! A.M.Y., 2001 Phenomenological models Large uncertainty!!! See J. Noronha-Hostler, arxiv:

64 Bulk viscosity S. Finazzo, R. Rougemont, H. Marrochio, JN, JHEP 1502 (2015) 051 The Kubo formula is Retarded correlator Infalling b.c. for metric fluctuations 64

65 Bulk viscosity S. Finazzo, R. Rougemont, H. Marrochio, JN, JHEP 1502 (2015) 051 Infalling boundary conditions: General formula Gubser, 2009 Smallish bulk visc. Parametrization for hydro 65

66 Bulk viscosity S. Finazzo, R. Rougemont, H. Marrochio, JN, JHEP 1502 (2015) 051 Small value for this transport coefficient in the QGP 66

67 Electric conductivity (still at zero chemical potential) S. I. Finazzo and J. Noronha, Phys. Rev. D 89, (2014). Model seems to be on the right track for thermodynamics and transport 67

68 Doping the holographic QGP with quarks R. Rougemont, J. Noronha-Hostler, JN, PRL Suppression of baryon diffusion and transport for collisions in the BES regime Baryon susceptibility Baryon conductivity 68 Baryon diffusion Thermal conductivity

69 Doping the holographic QGP with quarks R. Rougemont, A. Ficnar, S. Finazzo, R. Critelli, J. Noronha-Hostler, JN, PRD 2017 Baryon rich QGP is a perfect fluid (but a bad baryon conductor) Small bulk viscosity 69

70 Doping the holographic QGP with quarks Rougemont, Ficnar, Rougemont, Noronha, arxiv: [hep-th] (JHEP). Jet quenching parameter Charged black hole Predictions for light quark energy loss in a baryon rich medium Jets should be much more quenched at finite density 70