Download presentation

Presentation is loading. Please wait.

Published byHazel Caudle Modified over 2 years ago

1
Experiments Confront Theory Unicorn: the QGP Hunters: Experimentalists. Leaving theorists as...

2
http://www.anti-powerpoint-party.com

3
Experiments Confront Theory Theory: Effective theory for deconfinement, near T c. Today: only the “pure” glue theory (no dynamical quarks) Based upon detailed results from the lattice Experiment: No confrontation today... Soon: need to add quarks Present model may be the only real competition to AdS/CFT

4
The standard plot T→ ↑ T c SU(3) gauge theory without quarks, temperature T (Weakly) first order transition at T c ~ 290 MeV e/T 4 → ←3p/T 4 e(T)= energy density p(T)= pressure WHOT: Umeda, Ejiri, Aoki, Hatsuda, Kanaya, Maezawa, Ohno, 0809.2842

5
Another plot of the same Plot conformal anomaly, (e-3p)/T 4 : large peak above T c. ~ g 4 as T → ∞ ↑ T c T→ WHOT: Umeda, Ejiri, Aoki, Hatsuda, Kanaya, Maezawa, Ohno, 0809.2842 ∞

6
Strong vs weak coupling at T c ? Resummed perturbation theory at 3-loop order works down to ~ 3 T c. Intermediate coupling: α s (T c ) ~ 0.3. Not so big... So what happens below ~ 3 T c ? Want effective theory; e.g.: chiral pert. theory: expand in m π /f π, exact as m π → 0. But there is no small mass scale for SU(3) in “semi”-QGP, T c → 3 T c. →→→ Andersen, Su, & Strickland, 1005.1603

7
Perhaps α s is not so big at T c Braaten & Nieto, hep-ph/9501375 Laine & Schröder, hep-ph/0503061 & 0603048 From two loop calculation, matching original to effective theory: Pure gauge: α(7. T). 3 flavors of quarks: α(9. T). T c ~ Λ MS ~ 200 MeV. So α s eff (T) ~ α s eff (2 π T) ~ 0.3 at T c : not so big Grey band uncertainty from changing scale by factor 2. α(2πT)

8
Not strong coupling, even at T c QCD coupling runs like α(2πT), intermediate at T c, α(2πT c ) ~ 0.3 Braaten & Nieto, hep-ph/9501375, Laine & Schröder, hep-ph/0503061 & 0603048 HTL resummed perturbation theory, NNLO, good to ~ 8 T c : Andersen, Leganger, Strickland, Su, 1106.0514 Assume: not a strongly coupled QGP near T c ! versus: AdS/CFT....

9
What to expand in? Consider SU(N) for different N. # perturbative gluons ~ N 2 - 1. Scaled by ideal gas values, e and p for N = 3, 4 and 6 look very similar Implicitly, expand about infinite N. Explicitly, assume classical expansion ok N=3: Boyd et al, lat/9602007 N = 4 & 6: Datta & Gupta, 1006.0938 T→ N = 3, 4, 6 ↑ T c 4 T c ↑

10
Conformal anomaly ≈ N independent For SU(N), “peak” in e-3p/T 4 just above T c. Approximately uniform in N. Not near T c : transition 2nd order for N = 2, 1st order for all N ≥ 3 N=3: weakly 1st order. N = ∞: strongly 1st order (even for latent heat/N 2 ) Datta & Gupta, 1006.0938 long tail? ↑ T c 4 T c ↑ T→ N = 3, 4, 6

11
Tail in the conformal anomaly To study the tail in (e-3p)/T 4, multiply by T 2 /(N 2 -1) T c 2 : (e-3p)/((N 2 -1)T 2 T c 2 ) approximately constant, independent of N Datta & Gupta, 1006.0938 ↑ T c 4 T c ↑ T→ N = 3, 4, 6

12
Precise results for three colors From WHOT: 2 T c ↑ ↑ T c ↑ 1.2 T c T→ WHOT: Umeda, Ejiri, Aoki, Hatsuda, Kanaya, Maezawa, Ohno, 0809.2842

13
How to get a term ~ T 2 in the pressure? Expand pressure of ideal, massive gas in powers of mass m: Quasi-particle models: choose m(T) to fit pressure. Need m(T) to increase sharply as T → T c to suppress pressure. Inelegant... T→ m(T)↑ Above: Castorina, Miller, & Satz, 1101.1255 Originally: Peshier, Kampfer, Pavlenko & Soff, PRD 1996 t = T/T c, a =.47, b =.13, c =.39

14
A simple solution Our model: generalization of Meisinger, Miller & Ogilvie, ph/0108009 Dumitru, Guo, Hidaka, Korthals-Altes, & RDP, arXiv:1011.3820 + 1112.? Also: Y. Hidaka & RDP, 0803.0453, 0906.1751, 0907.4609, 0912.0940. Assume there is some potential, V(q). The vacuum, q 0, is the minimum of V(q): Pressure is the value of the potential at the minimum: For T > 1.2 T c, a constant ~T 2 in the pressure, is due to a constant ~T 2 in V(q): Above 1.2 T c, 〈 q 〉 = 0. Except near T c, for most of the semi-QGP, the non-perturbative part of the pressure, ~T 2, is due just to a constant Region where 〈 q 〉 ≠ 0, and V(q) matters, is very narrow: T: T c → 1.2 T c Unexpected consequence of precise lattice data. Large N: makes sense to speak of classical 〈 q 〉 instead of fluctuations.

15
An effective (matrix) model for deconfinement Lattice: SU(N) gauge theories, without quarks. Simulations show: N = 3 close to N = ∞. Not just the pressure. Simple matrix model, valid in large N expansion (no small masses). Fit to pressure for all N with 2 parameters Good agreement with interface tensions Disagrees with the (renormalized) Polyakov loop - ? New: adjoint Higgs phase, with split masses, for T < 1.2 T c. Unexpected: transition region very narrow, < 1.2 T c Generalization of Meisinger, Miller, Ogilvie ph/0108009, MMO Dumitru, Guo, Hidaka, Korthals-Altes, & RDP, arXiv:1011.3820 +... Also: Y. Hidaka & RDP, 0803.0453, 0906.1751, 0907.4609, 0912.0940.

16
What the lattice tells us Weak dependence on # colors Not just the pressure...

17
Hidden Z(2) spins in SU(2) Consider constant gauge transformation: As U c ~ 1, locally gluons invariant: Nonlocally, Wilson line changes: L ~ propagator for “test” quark. SU(3): det U c = 1 ⇒ j = 0, 1, 2 SU(N): U c = e 2 π i j/N 1: Z(N) symmetry. Z(N) spins of ‘t Hooft, without quarks Quarks ~ background Z(N) field, break Z(N) sym. N = 3

18
Hidden Z(3) spins in SU(3) T >> T c T ~ T c T < T c Im l↑ Re l→ Lattice, A. Kurkela, unpub.’d: 3 colors, loop l complex. Distribution of loop shows Z(3) symmetry: z Interface tension: box long in z. Each end: distinct but degenerate vacua. Interface forms, action ~ interface tension: T > T c : order-order interface = ‘t Hooft loop: measures response to magnetic charge Korthals-Altes, Kovner, & Stephanov, hep-ph/9909516 Also: if trans. 1st order, order-disorder interface at T c.

19
Usual spins vs Polyakov Loop T→ T c ↑ ↑ L = SU(N) matrix, Polyakov loop l ~ trace: Confinement: F test qk = ∞ ⇒ 〈 l 〉 = 0 Above T c, F test qk < ∞ ⇒ 〈 l 〉 ≠ 0 〈 l 〉 measures ionization of color: partial ionization when 0 < 〈 l 〉 < 1 : “semi”-QGP Svetitsky and Yaffe ’80: SU(3) 1st order because Z(3) allows cubic terms: Does not apply for N > 3. So why is deconfinement 1st order for all N ≥ 3?

20
Polyakov Loop from Lattice: pure Glue, no Quarks Lattice: (renormalized) Polyakov loop. Strict order parameter Three colors: Gupta, Hubner, Kaczmarek, 0711.2251. Suggests wide transition region, like pressure, to ~ 4 T c. T → ↑ ↑ ~ 4 T c ←1.0 ← ~ 0.4 ↑ T c ↑T=0 ← Confined →← SemiQGP→ ← “Complete” QGP →

21
Polyakov Loop from Lattice: Glue plus Quarks, “T c ” Quarks ~ background Z(3) field. Lattice: Bazavov et al, 0903.4379. 3 quark flavors: weak Z(3) field, does not wash out approximate Z(3) symmetry. ↑“T c ”.8“T c ”↑ 2 “T c ”↑ ← 0.2 ← Hadronic →← “Semi”-QGP →←Complete QGP ↑ ↑T=0 ←1.0 T →

22
Transition region narrow: for pressure, < 1.2 T c ! For interface tensions, < 4 T c... Above 1.2 T c, pressure dominated by constant term ~ T 2. What does this term come from? Gluon mass m(T)? But inelegant... SU(N) in 2+1 dimensions: ideal ~ T 3. Caselle +...: also T 2 term in pressure. But mass would be m 2 T, not m T 2. T 2 term like free energy of massless fields in 2 dimensions: string? Above T c ? Need to include quarks! Can then compute temperature dependence of: shear viscosity, energy loss of light quarks, damping of quarkonia... Skipping to the punchline

23
Lattice: SU(N) in 2+1 dimensions SU(N) in 2+1 dim’s for N = 2, 3, 4, 5, & 6. Below plot of T c /T, not T/T c. Clear evidence for non-ideal terms ~ T 2, not ~ T T c /T→ ↑10 T c ↑1.1T c ↑ 2T c Caselle, Castagnini, Feo, Gliozzi, Gursoy, Panero, Schafer, 1111.0580.

24
T→ ↑ T c deconf With quarks: “T c ” moves down: which T c ? Just glue: T c deconf ~ 290 MeV. Common lore: with quarks, one “T c ”, decreases. Matrix model: T c deconf does not change by addition of dynamical quarks. With light quarks, only chiral trans, when 〈 loop 〉 << 1. Hence T c chiral << T c deconf. ↑ T c chiral Lattice: Bazavov and Petreczky + HotQCD, 1110.2160 Ren’d loop ↑ With quarks ↓ ←without quarks ↑

25
Shear viscosity changes with T In semi-QGP, η suppressed from pert. value through function R(q). Not like kinetic theory Log sensitivity, through constant κ R (q): Y. Hidaka & RDP, 0912.0940. c pert : P. Arnold, G. Moore, and L. Yaffe, hep-ph/0010177, hep-ph/0302165 T/T c →

26
“Bleaching” of color near T c. Roughly speaking, as 〈 loop 〉 → 0, all colored fields disappear. Quarks, in fundamental rep. as 〈 loop 〉. Gluons, in adjoint rep., as 〈 loop 〉 2. Bleaching of color as T → T c : robust consequence of the confinement of color QGP: quarks and gluons. Semi-QGP: dominated by quarks, by ~ 〈 loop 〉 Why recombination works at RHIC but not at LHC? (v 2 /# quarks vs kinetic energy/# quarks) Suppression of color universal for all fields, independent of mass. Why charm quarks flow the same as light quarks? (single charm vs pions) An effective theory can provide a bridge from lattice simulations to experiment

27
Lattice: order-order interface tensions σ Lattice: de Forcrand & Noth, lat/0510081. σ ~ universal with N Semi-classical σ : Giovanengelli & Korthals-Altes ph/0102022; /0212298; /0412322: GKA ‘04 Above 4 T c, semi-class σ ~ lattice. Below 4 T c, lattice σ << semi-classical σ. Even so, when N > 3, all tensions satisfy “Casimir scaling” at T > 1.2 T c. ↑ T c 4.5 T c ↑ N = 4 Semi-classical↓ T→ ⇐ lattice

28
Other models Fit only the pressure, not interface tensions. Masses as T → T c + : some go up (massive gluons) some go down (Polyakov loops)

29
Models for the “s”QGP, T c to 4 T c 1. Massive gluons: Peshier, Kampfer, Pavlenko, Soff ’96...Castorina, Miller, Satz 1101.1255 Castorina, Greco, Jaccarino, Zappala 1105.5902 Mass decreases pressure, so adjust m(T) to fit p(T). Simple model. Gluons very massive near T c. 2. Polyakov loops: Fukushima ph/0310121...Hell, Kashiwa, Weise 1104.0572 Effective potential of Polyakov loops. Potential has 5 parameters... With quarks, at T ≠ 0, can go from μ = 0 to μ ≠ 0 3. AdS/CFT: Gubser, Nellore 0804.0434...Gursoy, Kiritsis, Mazzanti, Nitti, 0903.2859 Add potential for dilaton, φ, to fit pressure. Only infinite N. Relatively simple potential, 4. Monopoles: Liao & Shuryak, 0804.0255. Vortices: Tuesday: Takuya Saito

30
Matrix model: two colors Simple approximation Two colors: transition 2nd order, vs 1st for N ≥ 3 Using large N at N = 2

31
Matrix model: SU(2) Simple approximation: constant A 0 ~ σ 3, nonperturbative, ~ 1/g: Point halfway in between: q = ½, l = 0. Confined vacuum, L c, Classically, A 0 cl has zero action: no potential for q. Single dynamical field, q Loop l real. Z(2) degenerate vacua q = 0 and 1: x x x Re l→ 1 0

32
Potential for q, interface tension Computing to one loop order about A 0 cl gives a potential for q: Gross, RDP, Yaffe, ‘81 Use V pert (q) to compute σ: Bhattacharya, Gocksch, Korthals-Altes, RDP, ph/9205231. Balancing S cl ~ 1/g 2 and V pert ~ 1 gives σ ~ 1/√g 2 (not 1/g 2 ). Width interface ~ 1/g, justifies expansion about constant A 0 cl. GKA ‘04: σ ~... + g 2 1 0 x x x

33
Symmetries of the q’s Wilson line L not gauge invariant, L → Ω † L Ω. Its eigenvalues, e ± i π q, are. Ordering of L’s eigenvalues irrelevant. Symmetries: q → q + 2 : q angular variable. Valid with quarks. Pure glue: also, q → q + 1, Z(2) transf., L → - L For pure glue, can restrict q: 0 → 1. Then Z(2) transf. q → 1 - q: Z(2) transf., plus exchange of eigenvalues Any potential of q must be invariant under q → 1- q

34
Potentials for the q’s Add non-perturbative terms, by hand, to generate ≠ 0 : By hand? V non (q) from: monopoles, vortices... Liao & Shuryak: ph/0611131, 0706.4465, 0804.0255, 0804.4890 T < T c : 〈 q 〉 = ½ → 1 0 x x x 1 T >> T c : 〈 q 〉 = 0,1 → 0 x x x

35
Three possible “phases” Two phases are familiar: 〈 q 〉 = 0, 1: 〈 l 〉 = ± 1: “Complete” QGP: usual perturbation theory. T >> T c. 〈 q 〉 = 1/2: 〈 l 〉 = 0 : confined phase. T < T c Also a third phase, “partially” deconfined (adjoint Higgs phase) 0 T > T c x? Lattice: one transition, to confined phase, at T c. No other transition above T c. Still, there is an intermediate phase, the “semi”-QGP Strongly constrains possible non-perturbative terms, V non (q).

36
Getting three “phases”, one transition Simple guess: V non ~ loop 2, 1st order transition directly from complete QGP to confined phase, not 2nd Generic if V non (q) ~ q 2 at q << 1. Easy to avoid, if V non (q) ~ q for small q. Then 〈 q 〉 at all T > T c. Imposing the symmetry of q ↔ 1 - q, V non (q) must include x xx Term ~ q at small q avoids transition from pert. QGP to adjoint Higgs phase

37
Cartoons of deconfinement Consider: ⇓ a = ¼: semi QGP x x ⇓ a = 0: complete QGP x x a = ½: T c => Stable vacuum at q = ½ Transition second order x

38
Meisinger, Miller, Ogilvie ph/0108009: take V non ~ T 2 0-parameter matrix model, N = 2 Two conditions: transition occurs at T c, pressure(T c ) = 0 Fixes c 1 and c 3, no free parameters. But not close to lattice data (from ’89!) ↑ T c 3 T c ↑ T→ ⇐ 0-parameter model ⇐ Lattice Lattice: Engels, Fingberg, Redlich, Satz, Weber ‘89

39
1-parameter matrix model, N = 2 Dumitru, Guo, Hidaka, Korthals-Altes, RDP ‘10: to usual perturbative potential, Add - by hand - a non-pert. potential V non ~ T 2 T c 2. Also add a term like V pert : Now just like any other mean field theory. 〈 q 〉 given by minimum of V eff : 〈 q 〉 depends nontrivially on temperature. Pressure value of potential at minimum:

40
Lattice vs matrix models, N = 2 Choose c 2 to fit e-3p/T 4 : optimal choice Reasonable fit to e-3p/T 4 ; also to p/T 4, e/T 4. N.B.: c 2 ~ 1. At T c, terms ~ q 2 (1-q) 2 almost cancel. ↑ T c 3 T c ↑ T→ ⇐ Lattice ⇐ 0-parameter ⇐ 1-parameter Lattice: Engels, Fingberg, Redlich, Satz, Weber ‘89

41
Lattice vs 1-parameter model, N = 2 ↑ T c 3T c ↑ T→ ⇐ e-3p/T 4, lattice ⇐ e-3p/T 4, model ⇑ p/T 4, lattice ⇓ e/T 4, model ⇓ e/T 4, lattice ⇑ p/T 4, model

42
Width of transition region, 0- vs 1-parameter 1-parameter model: get sharper e-3p/T 4 because 〈 q 〉 -> 0 much quicker above T c. Physically: sharp e-3p/T 4 implies region where 〈 q 〉 is significant is narrow N.B.: 〈 q 〉 ≠ 0 at all T, but numerically, negligible above ~ 1.2 T c ; p ~ 〈 q 〉 . Above ~1.2 T c, the T 2 term in the pressure is due entirely to the constant term, c 3 ! ⇐ 0-parameter ⇓ 1-parameter ↑ T c 2 T c ↑T→

43
Polyakov loop: 1-parameter matrix model ≠ lattice Lattice: renormalized Polyakov loop. 0-parameter model: close to lattice 1-parameter model: sharp disagreement. 〈 l 〉 rises to ~ 1 much faster - ? Sharp rise also found using Functional Renormalization Group (FRG): Braun, Gies, Pawlowski, 0708.2413; Marhauser, Pawlowski, 0812.1144 ⇐ lattice ⇐ 0-parameter ⇓ 1-parameter ↑ T c T→ 2 T c ↑ Lattice: Cardoso, Bicudo, 1104.5432 Can reconcile by (arbitrary) shift in zero point energy

44
Interface tension, N = 2 σ vanishes as T→T c, σ ~ (t-1) 2ν. Ising 2ν ~ 1.26; Lattice: ~ 1.32. Matrix model: ~ 1.5: c 2 important. Semi-class.: GKA ’04. Include corr.’s ~ g 2 in matrix σ(T) (ok when T > 1.2 T c ) N.B.: width of interface diverges as T→T c, ~ √(t 2 - c 2 )/(t 2 -1). ↑ T c 2.8 T c ↑ T→ ⇐ matrix model Semi-classical ⇐ lattice Lattice: de Forcrand, D’Elia, Pepe, lat/0007034

45
Lattice: A 0 mass as T → T c - up or down? Kaczmarek, Karsch, Laermann, Lutgemeier lat/9908010 μ/T goes down as T → T c m D /T goes up as T → T c Cucchieri, Karsch, Petreczky lat/0103009, Kaczmarek, Zantow lat/0503017 Which way do masses go as T → T c ? Both are constant above ~ 1.5 T c. T→ Gauge invariant: 2 pt function of loops: Gauge dependent: singlet potential ↑ T c ↑ 2T c ↑ T c

46
Adjoint Higgs phase, N = 2 A 0 cl ~ q σ 3, so 〈 q 〉 ≠ 0 generates an (adjoint) Higgs phase: RDP, ph/0608242; Unsal & Yaffe, 0803.0344, Simic & Unsal, 1010.5515 In background field, A = A 0 cl + A qu : D 0 cl A qu = ∂ 0 A qu + i g [A 0 cl, A qu ] Fluctuations ~ σ 3 not Higgsed, ~ σ 1,2 Higgsed, get mass ~ 2 π T 〈 q 〉 Hence when 〈 q 〉 ≠ 0, for T < 1.2 T c, splitting of masses: ↑ T c T→ 1.5 T c ↑ ⇐ diagonal A 0 mode ⇐ off-diagonal A 0 modes At T c : m diag = 0, m off ~ 2 m pert. 1 → ↑ 1.2 T c m pert = √2/3 g T: m/m pert ~.56 at 1.5 T c, from V non.

47
Matrix model: N ≥ 3 Why the transition is always 1st order One parameter model

48
Path to Z(3), three colors SU(3): two diagonal λ’s, so two q’s: Z(3) paths: move along λ 8, not λ 3 : q 8 ≠ 0, q 3 = 0.

49
Path to confinement, three colors Now move along λ 3 : In particular, consider q 3 = 1: Elements of e 2π i/3 L c same as those of L c. Hence tr L c = tr L c 2 = 0: L c confining vacuum Path to confinement: along λ 3, not λ 8, q 3 ≠ 0, q 8 = 0.

50
Z(3) paths in SU(3) gauge For SU(3), two diagonal generators, Z(3) paths: q 8 ≠ 0, q 3 = 0: Three degenerate vacua, for q 8 = 0, 1, and 2. Move between vacua along blue lines, Re l→ Im l↑ x x x

51
Confining vacuum in SU(3) Alternately, consider moving along λ 3. In particular, consider q 3 = 1: L c is the confining vacuum, X : “center” of space in λ 3 and λ 8 Move from deconfined vacuum, L = 1, to the confined vacua, L c, along red line: Re l→ Im l↑ x x x x Elements of e 2π i/3 L c same as those of L c. Hence LcLc

52
General potential for any SU(N) For SU(N), Σ j=1...N q j = 0. Hence N-1 independent q j ’s, = # diagonal generators. At 1-loop order, the perturbative potential for the q j ’s is As before, assume a non-perturbative potential ~ T 2 T c 2 : Ansatz: constant, diagonal matrix i, j = 1...N

53
Path to confinement, four colors Move to the confining vacuum along one direction, q j c : (For general interfaces, need all N-1 directions in q j space) Perturbative vacuum: q = 0. Confining vacuum: q = 1. Four colors: General N: confining vacuum = uniform distribution for eigenvalues of L For infinite N, flat distribution.

54
Cubic term for all N ≥ 3, so transition first order No term linear in φ. Cubic term in φ for all N ≥ 3. Along q c, about φ = 0 there is no symmetry of φ → - φ for any N ≥ 3. Hence terms ~ φ 3, and so a first order transition, are ubiquitous. Special to matrix model, with the q i ’s elements of Lie algebra. Svetitsky and Yaffe ’80: V eff (loop) ⇒ 1st order only for N=3; loop in Lie group Also 1st order for N ≥ 3 with FRG: Braun, Eichhorn, Gies, Pawlowski, 1007.2619. Define φ = 1 - q, Confining point φ = 0

55
Cubic term for four colors Construct V eff either from q’s, or equivalently, loops: tr L, tr L 2, tr L 3.... N = 4: |tr L| 2 and |tr L 3 | 2 not symmetric about q = 1, so cubic terms, ~ (q - 1) 3. (|tr L 2 | 2 symmetric, residual Z(2) symmetry) Cubic terms special to moving along q c in a matrix model. Not true in loop model x ⇐ |tr L| 2 ⇐ |tr L 3 | 2 ⇑ q = 1 qc ⇒qc ⇒ ⇑.8 ⇑ 1.2

56
x ⇐ |tr L| 2 |tr L 3 | 2 ⇒ ⇑ q =1 qc ⇒qc ⇒ ⇑.8 ⇑ 1.2 Cubic term for four colors Asymmetric in reflection about q = 1 ⇔

57
Lattice vs 0- and 1- parameter matrix models, N = 3 Results for N=3 similar to N=2. 0-parameter model way off. Good fit e-3p/T 4 for 1-parameter model, Again, c 2 ~ 1, so at T c, terms ~ q 2 (1-q) 2 almost cancel. ↑ T c 3 T c ↑ T→ ⇐ 1-parameter ⇐ 0-parameter ⇐ Points: lattice Lattice: Bielefeld, lat/9602007 Datta & Gupta, 1006.0938

58
Lattice vs 1- parameter model, N = 3 ↑ T c 3T c ↑ T→ ⇐ e-3p/T 4, lattice ⇐ e-3p/T 4, model ⇓ e/T 4, lattice ⇓ e/T 4, model ⇑ p/T 4, lattice ⇑ p/T 4,model

59
Polyakov loop: matrix models ≠ lattice Renormalized Polyakov loop from lattice does not agree with either matrix model 〈 l 〉 - 1 ~ 〈 q 〉 2 : By 1.2 T c, 〈 q 〉 ~.05, negligible. Again, for T > 1.2 T c, the T 2 term in pressure due entirely to the constant term, c 3 ! Rapid rise of 〈 l 〉 as with FRG: Braun, Gies, Pawlowski, 0708.2413 ↑ T c T→2 T c ↑ ⇐ lattice ⇑ 0-parameter 1-parameter ⇓ Cannot reconcile by shift in zero point energy Lattice: Gupta, Hubner, and Kaczmarek, 0711.2251.

60
Interface tension, N = 2 and 3 Order-order interface tension, σ, from matrix model close to lattice. For T > 1.2 T c, path along λ 8 ; for T < 1.2 T c, along both λ 8 and λ 3. σ(T c )/T c 2 nonzero but small, ~.02. Results for N =2 and N = 3 similar - ? Semi-classical ⇐ matrix model, N = 2 ⇐ matrix model, N = 3 ↑ T c 5 T c ↑ T→ Lattice: de Forcrand, D’Elia, Pepe, lat/0007034 de Forcrand, Noth lat/0506005 lattice, N=3

61
Adjoint Higgs phase, N = 3 For SU(3), deconfinement along A 0 cl ~ q λ 3. Masses ~ [λ 3, λ i ]: two off-diagonal. Splitting of masses only for T < 1.2 T c : Measureable from singlet potential, 〈 tr L † (x) L(0) 〉, over all x. T/T c → ⇐ 4 off-diagonal, K’s ⇐ 2 off-diagonal, π’s ⇐ 2 diagonal modes At T c : m diag small, but ≠ 0 m pert = g T, m/m pert ~.8 at 1.5 T c, from V non.

62
Matrix model: N ≥ 3 To get the latent heat right, two parameter model. Thermodynamics, interface tensions improve

63
Latent heat, and a 2-parameter model Latent heat, e(T c )/T c 4 : 1-parameter model too small: 1-para.: 0.33. BPK: 1.40 ±.1 ; DG: 1.67 ±.1. 2-parameter model, c 3 (T). Like MIT bag constant WHOT: c 3 (∞) ~ 1. Fit c 3 (1) to DG latent heat Fits lattice for T < 1.2 T c, overshoots above. ↑ T c 3T c ↑ T→ ⇐ Lattice ⇐ 2-parameter ⇐ 1-parameter Latttice latent heat: Beinlich, Peikert, Karsch (BPK) lat/9608141 Datta, Gupta (DG) 1006.0938 Bag const ~ (262 MeV) 4 c 2 not near 1, vs 1-para.

64
Anomaly: 2-parameter model vs lattice ↑ T c 3T c ↑ T→ ⇐ Lattice ⇐ 2-parameter

65
↑ T c 3T c ↑ T→ ⇐ Lattice ⇐ 2-parameter Anomaly times T 2 : 2-parameter model vs lattice

66
Thermodynamics of 2-parameter model, N = 3 ⇐ e-3p/T 2 T c 2, lattice ⇓ e-3p/T 2 T c 2, model ⇑ p/T 4, lattice ⇓ e/T 4, lattice ⇓ e/T 4, model T/T c →

67
Interface tensions, 2-parameter model, N = 3 Order-order interface tension, σ, close to lattice. Order-order σ(T c )/T c 2 ~.043. 1st order transition, so can compute order-disorder σ(T c )/T c 2 ~.022, vs Lattice: Lucini, Teper, Wenger, lat/0502003,.019 Beinlich, Peikert, Karsch lat/9608141 0.16 ↑ T c 5 T c ↑ lattice, N=3 ⇓ ⇑ 2-parameter model, N=3 lattice, N=2 ⇓ Lattice: de Forcrand, D’Elia, Pepe, lat/0007034 de Forcrand, Noth lat/0506005 Order-order σ: T→

68
2-parameter model, N = 4 Assume c 3 (∞) = 0.95, like N=3. Fit c 3 (1) to latent heat, Datta & Gupta, 1006.0938 Order-disorder σ(T c )/T c 2 ~.08, vs lattice,.12, Lucini, Teper, Wenger, lat/0502003 T/T c → ⇑ p/T 4, lattice ⇑ p/T 4, model ⇓ e/T 4, lattice ⇓ ⇓ e/T 4, model ⇐ e-3p/T 2 T c 2, lattice ⇓ e-3p/T 2 T c 2, model

69
2-parameter model, N = 6 ⇑ p/T 4, lattice Order-disorder σ(T c )/T c 2 ~.25, vs lattice,.39, Lucini, Teper, Wenger, lat/0502003 T/T c → ⇑ p/T 4, model ⇓ e/T 4, lattice ⇓ ⇓ e/T 4, model ⇐ e-3p/T 2 T c 2, lattice ⇓ e-3p/T 2 T c 2, model

70
Matrix model, G(2) gauge group G(2): no center, yet has “confining” trans: Holland, Minkowski, Pepe, Wiese, lat/0302023 Very strong constraint on matrix model: we predict broad conformal anomaly/T 4. Pressure in G(2) not like pressure in SU(N), but interface tension

Similar presentations

OK

1 A Model Study on Meson Spectrum and Chiral Symmetry Transition Da

1 A Model Study on Meson Spectrum and Chiral Symmetry Transition Da

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on cadbury india ltd Ppt on l&t company Ppt on chapter 3 drainage cap Free ppt on types of houses Marketing mix ppt on sony tv Ppt on history of capital market in indian Ppt on council of ministry of nepal Authority of the bible ppt on how to treat Ppt on traction rolling stock trains Ppt on articles of association sample