N=4 super Yang-Mills Plasma
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1 N= suer Yn-Mlls Plsm ln Czj Insttute o Physs, Jn Kohnows Unversty, Kele, Poln bse on:. Czj & St. Mrówzyńs, Physl Revew D Czj & St. Mrówzyńs, Physl Revew D Czj & St. Mrówzyńs, Physl Revew D Feb 01, Shlmn Wnter Shool 1
2 Outlne 1. Motvton. N= suer Yn-Mlls. Bs lsm hrtersts. Colletve moes Dserson equtons Perturbtve omutton o sel-eneres Eetve ton 5. Collsonl hrtersts Elementry roesses Trnsort oeents Enery loss & qˆ 6. Conlusons 7 Feb 01, Shlmn Wnter Shool
3 Motvton Suersymmetry symmetry o Nture suersymmetr lsm s n nterestn objet o Nture tool or S/CFT ulty Grvty n S CFT: N = suer Yn-Mlls QCD vs. suer Yn-Mlls? 7 Feb 01, Shlmn Wnter Shool
4 Motvton ont. Does rumentry SUSY nue nstbltes n ermon setor? QED PLSM SUSY QED PLSM There re unstble hoton moes SUSY re there unstble hotno moes? 7 Feb 01, Shlmn Wnter Shool
5 7 Feb 01, Shlmn Wnter Shool j b j j b j b B b B e be Y X D D D F F L Lrnn o N= suer Yn-Mlls 1,,,, 1,,,,5,6, 0,1,,, j B N N N Rne o the el s ne Sn Number o erees o reeom Tye o the el - vetor - rel seuo-slr - Mjorn snor 5
6 Bs lsm hrtersts QGP N= SYMP enery ensty - ε T 60 N 1 7N N T N 1 rtle ensty - n T N 1 N N 1 T N 1 Debye mss - m D T 6 N N T N lsm rmeter - λ 1 r D n ll heml otentls re ssume to vnsh n both QGP n N= SYMP. 7 Feb 01, Shlmn Wnter Shool 6
7 Colletve moes 7 Feb 01, Shlmn Wnter Shool 7
8 Dserson equton Equtons o moton Dserson equtons Gluon el : et[ ] 0, Fermon el : et[ ˆ ] 0 ˆ Slr el : P 0,, P - retre sel-eneres whh esrbe nterton o resetve el wth surrounn lsm Solutons o the equtons - 7 Feb 01, Shlmn Wnter Shool olletve moes 8
9 Contrbutons to retre olrzton tensor n N= SYMP b N b Tr[ S S sym S sym S ] For every loo n tole there re nlol ormuls 7 Feb 01, Shlmn Wnter Shool 9
10 Hr Loo romton Wvelenth o qus-rtle s muh ber thn nter-rtle stne n the lsm: λ The only mensonl rmeter n ree ultrreltvst equlbrum lsm s temerture T. 1 1 ~ ~ T ~ ~ momentum o lsm onsttuent 1 ~ COLLECTIVE MODES: wve vetor o olletve moe 7 Feb 01, Shlmn Wnter Shool 10
11 the sme struture s n QED, SUSY QED n QCD symmetr trnsversl 7 Feb 01, Shlmn Wnter Shool 0 ] [ E N b b 0 Gue neenene! Polrzton tensor 6 8 s n n n 11 Eet o SUSY: vuum ontrbuton vnshes the oeents n ront o the strbuton untons re the numbers o erees o reeom q q QGP n n N N n
12 7 Feb 01, Shlmn Wnter Shool 0 ˆ E N j b j b The ermon sel-enery hs the sme struture or the N= SYM, QCD, SUSY QED n usul QED lsm. 0 ˆ E e e QED Fermon sel-enery 6 8 s n n n 1
13 Slr sel-enery Slr sel-enery: P B B b N b E n 8n 6n neenent o vnshes n the vuum lmt s 7 Feb 01, Shlmn Wnter Shool 1
14 7 Feb 01, Shlmn Wnter Shool 1 1 HL HL HL HL D D DΨ Ψ F F L L L L y y y L S Sel-enery onstrns the orm o eetve ton ], [, y S y Hr loo eetve ton 1
15 7 Feb 01, Shlmn Wnter Shool Struture o eh sel-enery s unque HL F D F E N b b L HL D E N b b L HL E N L The struture o eh term o the eetve ton ers to be unque From eetve ton to sel-eneres 15
16 Colletve moes The setrum o olletve ettons o ue bosons, ermons n slrs n N= suer Yn-Mlls, QCD, QED n SUSY QED lsm s the sme. ue bosons - whole vrety o ossble olletve ettons, n rtulr there re unstble moes ermons there s no unstble ettons slrs olletve moes re s rel, mssve rtles P m e E m e 7 Feb 01, Shlmn Wnter Shool 16
17 Collsonl hrtersts 7 Feb 01, Shlmn Wnter Shool 17
18 Elementry roesses Coulomb-le sttern S. C. Huot, S. Jeon, n G. D. Moore, Phys. Rev. Lett. 98, Feb 01, Shlmn Wnter Shool 18
19 Trnsort oeents Collsonl roesses trnsort roertes o ultrreltvst lsm temerture s the only mensonl rmeter oulomb-le nterton omntes the ynms o the system sher vsosty T ln ~ 1 S. C. Huot, S. Jeon, n G. D. Moore, Phys. Rev. Lett. 98, Feb 01, Shlmn Wnter Shool 19
20 Enery loss n momentum broenn re not onstrne by mensonl ruments E ~ T, ET, E, qˆ ~ T, ET, E T, E, een on se sttern roess uner onserton 7 Feb 01, Shlmn Wnter Shool 0
21 Cross setons o bnry ntertons n SUSY QED 7 Feb 01, Shlmn Wnter Shool 1
22 Enery loss n momentum broenn n SUSY QED lsm seletron s trversn n equlbrum hoton s. M e E e T T E ET e T 5 qˆ e 1 T 5 T E ET e 1 T 7 Feb 01, Shlmn Wnter Shool
23 Comrson wth Coulomb-le nterton Enery loss or ontt nterton E e T 5 Enery loss or Coulomb-le nterton E e E T ln et E. Brten n M. H. Thom, Phys. Rev. D, Feb 01, Shlmn Wnter Shool
24 enery hne n snle ollson ross seton ensty nverse men th enery loss Enery loss E 1 E ~ E Contt Coulomb s t M ~ e M ~ e ~ E e ~ ET ~ T ~ e T E ~ e T ~ e T ~ T e ~ T ~ e T ~ e T Derent ntertons le to the sme enery loss! 7 Feb 01, Shlmn Wnter Shool
25 Conlusons The olletve moes o N= suer Yn-Mlls lsm re the sme s those o QGP. There re no unstble ermon moes. The strutures o sel-eneres er to be unque. The trnsort hrtersts o SUSY lsm re smlr to those o QGP. Both systems re very smlr to eh other n the we ouln reme. 7 Feb 01, Shlmn Wnter Shool 5
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