Deconfinement phase transition in SU(3)/Z3 QCD (adj) via the gauge theory/affine XY-model duality

Transcription

1 Dconfnmnt phas transton n SU(3)/Z3 QCD (adj) va th gaug thory/affn XY-modl dualty MOHAMED ABER UIVERSITY OF TOROTO TH W O R K S H O P O O - P E R T U R B A T I V E Q C D M.A., Erch Popptz, Mthat Unsal arxv:.6389 M.A., Scott Collr, Erch Popptz arxv:.84 /5/03

2 LHC LHC xctng nws?!! /5/03

3 Motvaton spontanous brakng of chral symmtry (va confnmnt) th vsbl mass n th unvrs 3 Confnmnt s th mchansm for holdng quarks nsd nuclons V R /5/03

4 Confnmnt s Hard! 4, SFSU Physcs Colloquum 4/5/03

5 Motvaton As w ncras th tmpratur, dconfnmnt happns Quark-gluon plasma: a nw stat of mattr ovl phnomna,.g. chral magntc ffct 5 /5/03

6 Phas transton ordr paramtrs Studyng phas transton (magntzaton m ) Ordr paramtr Th physcs s that Ths s attrbutd to xp A0 dx s cntr symmtry n SU() 0 Confnd phas tr[ ] 0, T T c Dconfnd phas tr 0, T tr[ ] Z 6 F T ~ / 0 ordr paramtr tr Tc Thrmal crcl: compact tm T c T crcumfr nc /5/03

7 Phas transton ordr paramtrs 7 Dvd by th cntr Stll transton SU ( ) / tr Z jumps at th U tr 0 T c U SU( ) / Z Z Topologcal group SU() /5/03

8 Gaug thors on, R S Lattc QCD s n xcllnt agrmnt wth ths pctur QCD s a strongly coupld systm, not analytcally tractabl Ways AdS/CFT On nds a smplr thory that s undr complt control, yt rsmbls th orgnal thory, A promsng stup s Yang-Mlls on R S Ths das startd n th 990 n suprsymmtry 8 Spatal crcl /5/03

9 Pros: Gaug thors on, R S Prform rlabl sm-classcal calculatons Tst th ruls of dffrnt symmtrs (cntr, topologcal, chral, tc.) Dsntangl dffrnt physcal phnomna (.g. confnmnt & chral symmtry brakng) Mappng to lowr-dmnsonal condnsd mattr systms (smulatons, or usng analogu systms to tst our guag thors) FU!!!! 9 /5/03

10 Gaug thors on Cons: ot th ral world Larg L lmt s not undr control 0, R S /5/03

11 Gaug thors on, R S Ultmat goal Cook up modls that contan th sam ngrdnts of ralstc thors (adjont & fundamntal frmons, magntc fld, th vacuum angl, tc) Compar th rsults wth xstng xprmnts (thr ral or full 4-D lattc xprmnts) Mak prdctons and propos furthr xprmnts /5/03

12 Gaug thors on, R S Today s mal: dconfnng phas transton n SU(3)/Z_3 QCD wth adjont frmons Adj frmons QCD tr[] Lattc xprmnts for SU(3) modl wr conductd n 4-D : frst ordr transton Karsch and Lutgmr 998 /5/03

13 Gaug thors on, R S Dconfnng phas transton of SU() (adj) gaug thors wth on compact dmnson va gaug thory/affn XY modl dualty M.A., E. Popptz, M. Unsal 0, M.A., S.C., E. Popptz 0 H A. x x cos B. J cos, x SU() & SU()/Z usng RG (scond ordr transton) SU(3)/Z3 usng Mont Carlo x 3 x /5/03

14 Outln: 4, Formulaton of QCD adj on R S, prtubatv and non-prturbatv ffcts at T=0 and Coulomb gas QCD adj at fnt tmpratur, partton functon Mappng to XY spn-modls Mont Carlo Smulatons Concluson and futur drctons /5/03

15 QCD adj on, R S 5, Formulaton S R, S g tr - F F tr I D I SU( n f ) U() Flavor symmtry small S R, L g tr- F j F n f j Adjont frmons wth prodc boundary condtons along th crcl g D A V ( A ) 4 Compact scalar ff S 4 On-loop ffct Z symmtry /5/03

16 QCD adj on, R S, prturbatv tratmnt 6 Th thory ablanzs at small S SU( ) th gaug couplng s small Th thory s ffctvly 3-D g(e) U() n f 4 / L SU() Strong couplng scal E S U() W and havy chargd frmons g I I, L 4 R componntsof O L dual photons masslss frmons /5/03

17 on-prturbatv objcts Mor ntrstng story to tll: non-prturbatv ffcts (Polyakov modl) Fynman path ntgral Z Eucld 7 paths S E Prturbatv +non-prturbatv (nstantons) Monopol-nstantons /5/03

18 on-prturbatv objcts Ths nstantons ar localzd n spac and tm 8 probablty S S 0 0 / 8 g Intrnal structur, thy lv n th Dynkn spac SU() ormal monopol Affn root Twstd monopol /5/03

19 on-prturbatv objcts Twstd monopols wr dscovrd by Kraan and Baal and (calarons), and L and Lu (D-brans) (998) 9 / L S ormal Twstd ORM ORM - TWIST TWIST - S 0 /. S 0 /. S 0 /. S 0 /. /5/03

20 on-prturbatv objcts But w hav addtonal adjont frmons 0 S 0 /. dt IJ I J S 0 /. dt IJ I J S0 /. dt IJ I J S0 /. dt IJ I J /5/03

21 on-prturbatv objcts If nothng ls S R 3 L g S /. ( x) b dt I I 0 h.c. IJ I J o confnmnt! Howvr, for n f th thory s suprsymmtrc. Suprsymmtrc thors on 3 R S confn. (Khoz t al 999) Soluton by Unsal 007, mchansm s transcndnt byond SUSY /5/03

22 Molcular objcts (Bons) Bons can form n th vacuum. j, j, j, j bon( - - ) /5/03

23 Molcular objcts (Bons) 3 Forcs and scals V L r 4n log f g r L Coulomb frmons hoppng n f L g / L S0 Q. ( x), Q Q /5/03

24 QCD adj: Confnmnt 4 Bons prolfrat n th vacuum: 3-D Coulomb gas Q Q Q Q Q S Q L S 0 R 3 /3 L Q g 4 Q Q S c cos Q. frmons V Q mass trm 0 Q 4LQ. Q j g r Q Q Q Polyakov 977 Q /5/03

25 symmtrs Th U() chral s anomalous. Ths symmtry braks to SU() Z n f I D I SU( n f ) U() 5 U() SU() t Hooft vrtx for SU() dt S x + 0 /. ( ) IJ I J Rlvant symmtrs for confnmnt/dconfnmnt. Z dscrtchral Z cntr for SU( ), or topoologcalfor SU( )/ Z /5/03

26 QCD adj at fnt tmpratur At fnt tmpratur w compactfy th tm drcton L 6 /T LT R dntfd L g Q L S 0 /3 Q /T /5/03

27 QCD adj at fnt tmpratur 7 For L g S 0 /3 T L w can sum up mags Q Q Q Q Q Q Q T T 0 T T 3 T Q. Q j g r Q. Q g j log r /5/03

28 QCD adj at fnt tmpratur Story has an othr twst! At fnt tmpratur, th W s ar mportant 8 dnsty m W /T lctrc fugacty W r W j g LT. j log r /5/03

29 QCD adj at fnt tmpratur Add to that th Aharonov-Bohm ffct W 9 j Q T Q T Q 0 Q T Q T Q 3 T Q dx tm crcl 0 A 0 bon. Q x x j W bon /5/03

30 QCD adj at fnt tmpratur 30 Coulomb gas j Q j Q j log r Q Q Q Q Q Q j j j j Q Q j Q j Q j j Q Q log r j Q j j j /5/03

31 QCD adj at fnt tmpratur Th corrct partton functon B A b ja j A a j j B A j j b a j a A A a Q W W bon bon R R Q R R LT g R R Q Q g LT R d R d Z W W bon bon W W W bon bon bon,,,, 4/,,,. log. log. 8 xp!!!!,, Potntal sgn problm for smulatons bon W j Q Q j SU, dualty. 3. (3) For Strong couplng at th slf-dual pont /5/03 3

32 Mappng QCD adj to spn modls Cook agan, but now wth dffrnt lookng ngrdnt 3 ( x). v. ( x) Spn modl. ( x). (0) /5/03

33 Spn modl For SU(), thr s an xact soluton va RG analyss (M.A., E. Popptz, M. Unsal) Howvr, th RGEs brak down for SU(3) and so w must turn to smulatons on th lattc Th spn modl dual to thory of two coupld XY-spns: 33 s th /5/03

34 Spn modl Th spn modl s dfnd by a lattc partton functon wth: 34 Kntc trm: smlar to a modl usd to dscrb mltng of a d crystal on a trangular lattc (lson, 977) (Kardar, Statstcal Physcs of Flds) /5/03

35 Spn modl SU(3) ntrprtaton of spn modl: Fluctuatons n : duals of two masslss photons sourcd by magntc bons Vortcs dl. dscrb lctrc xctatons n thory (W-bosons) xctd at T > 0 Exact symmtry (corrspondng to two dual photons) s brokn by potntal xtrnal fld trm to symmtry 35 /5/03

36 Computatonal rsults: ordr paramtr 36 /5/03

37 Computatonal rsults: nrgy pr spn 37 /5/03

38 Computatonal rsults: vortx dnsty 38 Rcall: vortcs n th spn modl ar dual to lbratd W-bosons n th gaug thory /5/03

39 Pctur for QCD adj 39 T T c - + Q. ( x) Q. (0) - + T T c j. ( x) j. (0) j - + strng x Q j Q Q - + Q Q Q Q Q j + j - + j j - j j j j /5/03

40 Computatonal rsults: magntc suscptblty 40 /5/03

41 Computatonal rsults: spcfc hat 4 /5/03

42 Fnt-sz scalng 4 /5/03

43 Fnt-sz scalng Our fndngs appar consstnt wth a frst-ordr phas transton! Computatonal fnt-sz scalng provds a ncssary countrpont to th suggston of (unconvncng, du to th onst of strong couplng) rnormalzaton group analyss that th slf-dual pont s a fxd pont 43 /5/03

44 Enrgy probablty dstrbuton Furthr corroboraton for th obsrvd frst-ordr phas transton: phas coxstnc 44 Blow crtcal tmpratur Abov crtcal tmpratur /5/03

45 Enrgy probablty dstrbuton Phas coxstnc at th crtcal tmpratur: 45 /5/03

46 Fnal chck: Fnt-sz scalng 46 It has bn shown that for suffcntly larg volums and n th crtcal rgon s xpctd to b a unvrsal functon of /5/03

47 Concluson Study of th phas transton n th XY-spn modl, dual to QCD adj thory on R S Th phas transton s frst ordr for SU(3)/Z_3 usng Mont carlo smulatons Ths agrs wth what was found for th dconfnmnt transton n SU(3) 4-D QCD(adj) (wth n f = 4) On would also want to study othr ffcts, lk addng fundamntal frmons and turnng on a background fld Work along ths lns s n progrss, SFSU Physcs Colloquum 47 4/5/03

48 Spculatons and furthr studs 48 n f 5 /5/03