Quarks, Gluons and Black Holes BH David Mateos ICREA & University of Barcelona
Q uantum C hromo D ynamics... ... is the quantum theory of the strong nuclear force.
• Responsible for binding quarks inside mesons and baryons: q ¯ q q q q π 0 , π ± , . . . p , n , . . .
• Quarks interact because they carry colour, which they exchange through gluons: quark quark gluon • Analogue of electric charge, but comes in N c = 3 types: { q, q, q }
Why is QCD hard? • Strength of interaction depends on energy: λ 1 ( E ) Λ QCD ∼ 200 MeV
Why is QCD hard? Strong coupling: No analytic and truly systematic methods! λ Asymptotic freedom The Nobel Prize in Physics 2004 1 D. Gross D. Politzer F. Wilczek ( E ) Λ QCD ∼ 200 MeV
QCD remains a challenge after 36 years • Lattice is good for static properties, but not for real - time physics... • ... and for a theorist it is a black box. • A string reformulation might help. • Topic of this talk, with focus on the QGP .
Plan for the rest of the talk • All you need to know about string theory. • Why and how should QCD and ST be related. • Some results from ST ( a biased list ) : 200 Focus on deconfined phase 175 Quark � gluon plasma at . T > T c , µ B = 0 Temperature � MeV � 150 125 � � • Experimentally studied in HIC. 100 75 • Greatest impact from string theory. Hadron phase 50 2SC 25 CFL NQ More briefly on the vacuum: 250 500 750 1000 1250 1500 Baryon chemical potential � MeV � T = 0 , µ B = 0 � � • Obvious importance. µ B � = 0 Remarks on � � • Concluding thoughts.
All you need to know about string theory
• String theory is a quantum theory of one - dimensional objects.
• String theory is a quantum theory of one - dimensional objects. • Characterised by two parameters: g s � s
• Di ff erent vibration modes behave as particles of di ff erent masses and spins: M M=0, Spin=2: Graviton! BH
• Interested in strings propagating in curved space: � s R • Complicated theory, but simplifies dramatically if: � s � R : String behaves as a point. g s � 1 : String does not split. Classical supergravity.
• Also contains open strings... attached to D - branes. Closed strings Open strings D - branes
Why and how should QCD and string theory be related
The gauge/string duality + ... + • Large - N c expansion: ‘t Hooft ‘74 g s = 1 N c • First concrete example: Maldacena ‘97 � s N = 4 SYM ↔ IIB on AdS 5 × S 5 g s = 1 R 4 = λ� 4 R , s N c • Solvable string limit: N c → ∞ , λ → ∞ Framework for non - perturbative gauge theory physics! � � Disclaimer I: Not proven, but lots of evidence.
Why have we not solved QCD? N =4 SYM # Λ QCD ∼ Me − λ ( M ) ∼ M Decoupling: λ ( M ) ≪ 1 ≪ Supergravity: E λ ( M ) ≫ 1 Disclaimer II: Dual of QCD is presently inaccessible. Λ QCD
Therefore: • Certain quantitative observables ( eg. T=0 spectrum ) will require going beyond supergravity. • However, certain predictions may be universal enough to apply in certain regimes.
Some results from string theory: The QGP 200 175 Quark � gluon plasma Temperature � MeV � 150 125 100 75 Hadron phase 50 2SC 25 CFL NQ 250 500 750 1000 1250 1500 Baryon chemical potential � MeV �
Confinement... q, q, q, q } { q, q, q } ¯ q ¯ q ¯ q q, q, { q, Mesons and baryons
Confinement and Deconfinement q, q, q, q } { q, q, q } ¯ q ¯ q T c ∼ 175 MeV ¯ q q, q, { q, Mesons and baryons Quark Gluon Plasma ( QGP )
• This was realised in the hot, early Universe...
• This was realised in the hot, early Universe... ... and is the only fundamental phase transition that can be recreated in a lab like RHIC or LHC!
s = 1 Good example: η 4 π 16.0 � SB /T 4 14.0 � /T 4 Lattice thermodynamics: 12.0 10.0 E deconf ∼ 80% E ideal 8.0 6.0 3 flavour 2+1 flavour 4.0 Interpretation: 2 flavour 2.0 QGP is weakly coupled T/T c 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Karsch, hep - lat/0106019 Conclusion: η 1 s ∼ η /s must be large, since in pQCD Arnold, Moore & Y a ff e λ 2 log λ Huot, Jeon & Moore But, isn’t this counterintuitive?
Indeed, thermodynamics can be misleading... • For example, for N=4 SYM: E strong coupling ∼ 75% E ideal Gubser, Klebanov & Peet • And yet, in the limit one finds: N c → ∞ , λ → ∞ � � s = 1 η Policastro, Son & Starinets ’01 4 π Kovtun, Son & Starinets ‘03 • Similar statics, radically di ff erent dynamics. • Same for all non - Abelian plasmas with gravity dual in the limit : N c → ∞ , λ → ∞ � � - Theories in di ff erent dimensions. - With or without fundamental matter. - With or without chemical potential, etc.
• Suggests that is a “universal” property of η /s = 1 / 4 π strongly coupled non - Abelian plasmas, and hence... a prediction: If QCD just above deconfinement is strongly coupled, then . η /s � 1 / 4 π • W e cannot compute this, but we can go to RHIC:
� s ∼ 1 η 1 Results indicate strong coupling and . 4 π � � s ∼ 380 × 1 η For water . 1 4 π s ∼ 9 × 1 η For liquid He . 1 4 π Animation by Jeffery Mitchell (Brookhaven National Laboratory). Simulation by the UrQMD Collaboration
RHIC Scientists Serve Up “Perfect” Liquid New state of matter more remarkable than predicted -- raising many new questions April 18, 2005 Also of great interest to many following progress at RHIC is the emerging connection between the collider’s results and calculations using the methods TAMPA, FL -- The four detector groups conducting of string theory , an approach that attempts to explain fundamental research at the Relativistic Heavy Ion Collider (RHIC) -- a properties of the universe using 10 dimensions instead of the usual three giant atom “smasher” located at the U.S. Department of spatial dimensions plus time. Energy’s Brookhaven National Laboratory -- say they’ve created a new state of hot, dense matter out of the quarks “The possibility of a connection between string theory and RHIC collisions and gluons that are the basic particles of atomic nuclei, but is unexpected and exhilarating,” Dr. Orbach said. “String theory seeks to it is a state quite different and even more remarkable than unify the two great intellectual achievements of twentieth-century physics, had been predicted. In peer-reviewed papers summarizing general relativity and quantum mechanics, and it may well have a profound the first three years of RHIC findings, the scientists say that impact on the physics of the twenty-first century.” instead of behaving like a gas of free quarks and gluons, as was expected, the matter created in RHIC’s heavy ion collisions appears to be more like a liquid . Secretary of Energy Samuel Bodman Dr. Raymond L. Orbach
Why is the ratio universal? Deconfined plasma BH Witten ‘98 s = A Entropy: 4 G η = σ abs ( ω → 0) A = Viscosity: 16 π G 16 π G gauge/gravity duality classical GR theorem
� � Combine with another universal property Glueballs N f ≪ N c quark flavours BH � Karch & Randall ’01 � Karch & Katz ‘02 � � ¯ q � � Free quarks Mesons ���� ���� � � � � � � � � � � � � � � � � � � � � � �
Limiting velocity for mesons D.M., Myers & Thomson ‘07 Ejaz, Faulkner, Liu, Rajagopal & Wiedemann ‘07 Limiting velocity = Local speed of light at the tip
Peak in photon spectrum D.M., Patiño - Jaidar ’07 Casalderey - Solana, D.M. ‘08 ω ∼ v | � ω = | � k | k | v < 1 ω 2 = k 2 Meson with has same Rest quantum numbers as a photon mass Produces resonance peak in photon 2 - point function and hence in thermal photon spectrum: � J EM µ J EM ν � ∼ γ γ
Peak in photon spectrum • This is interesting because QGP is optically thin → Thermal photons carry valuable information. γ
Peak in photon spectrum • Eg. a simple model for J/ Ψ at LHC energies yields: 2 T diss = 1 . 25 T c 1.75 1.5 Thermal background 1.25 N γ from light quarks 1 0.75 J/ Ψ signal 0.5 0.25 3.5 4 4.5 5 5.5 6 ω [GeV] c ¯ c • Quadratically sensitive to cross - section -- not observable at RHIC. • Location of the peak between 3 - 5 GeV .
Peak in photon spectrum • Signal is also comparable ( or larger ) than pQCD background: Arleo, d’Enterria and Peressounko ‘07 -2 Pb-Pb +X, 5.5 TeV [0-10% central] dy) (GeV/c) � � 3 10 Total : prompt + thermal � Prompt: NLO N , E = 50 GeV � � 2 10 coll c loss Thermal: QGP 10 Thermal: HRG 2 T dp T ( � =0.1 fm/c) = 650 MeV 1 0 0 � N/( -1 10 2 d -2 10 -3 10 -4 10 -5 10 -6 10 -7 10 0 1 2 3 4 5 6 7 8 p (GeV/c) T
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