N=4 super Yang-Mills Plasma

Transcription

1 N= suer Yng-Mills Plsm Alin Czjk Institute o Physis, Jn Kohnowski University, Kiele, Polnd bsed on: A. Czjk & St. Mrówzyński, rxiv: [he-th] A. Czjk & St. Mrówzyński, Physil Review D A. Czjk & St. Mrówzyński, Physil Review D

2 Outline 1. Motivtion. N= suer Yng-Mills. Bsi lsm hrteristis. Colletive modes Disersion equtions Perturbtive omuttion o sel-energies Eetive tion 5. Collisionl hrteristis Elementry roesses Trnsort oeiients Energy loss & 6. Conlusions qˆ

3 Motivtion Suersymmetry symmetry o Nture suersymmetri lsm is n interesting objet o Nture tool or AdS/CFT dulity Grvity in AdS CFT: N = suer Yng-Mills QCD vs. suer Yng-Mills?

4 Motivtion Does rudimentry SUSY indue instbilities in ermioni setor? QED PLASMA SUSY QED PLASMA There re unstble hoton modes SUSY Are there unstble hotino modes?

5 j b ij i j b ij i b d B A b B A de be A A i i Y i X g i g D D D i F F L Lgrngin o N= suer Yng-Mills 1,,,, 1,,,,5,6, 0,1,,, j i B A N N N Rnge o the ield s index Sin Number o degrees o reedom Tye o the ield i A A - vetor - rel seudo-slr - Mjorn sinor 5

6 Bsi lsm hrteristis QGP N= SYMP energy density - ε T 60 N 1 7N N T N 1 rtile density - n T N 1 N N 1 T N 1 Debye mss - m D g T 6 N N g T N lsm rmeter - λ 1 r D n 0.0g 0.57g All hemil otentils re ssumed to vnish in both QGP nd N= SYMP. 6

7 Colletive modes 7

8 Gluon disersion eqution Eqution o motion o gluon ield A μ k [ k g k k k] A k k, k 0 Disersion eqution det[ k g k k k] Colletive modes - solutions: k 0 Π μν k - retrded olriztion tensor Intertion o gluon with surrounding lsm 8

9 Fermion nd slr disersion equtions Fermion ield: det[ kˆ k] 0 P k Slr ield: 0 k kˆ k 9

10 Keldysh Shwinger ormlism Desrition o non-equilibrium mny-body systems ig x, y de ~ T x y... Tr[ ˆ t...] T ~ - ordering long the ontour: ~ TA x B y x, y A x B y y, x B y A x 1 Contour Green untion o slr ield t 0 t mx t 10

11 Polriztion tensor Dyson Shwinger eqution: D D0 D0D Full ontour rogtor Free ontour rogtor Contour olriztion tensor D x, y D x y Homogeneity, trnsltionl invrine 11

12 Lowest order ontributions to Пx,y Contour ordered Green untions hve erturbtive exnsion similr to tht o time-ordered Green untions. Fermion loo Contour olriztion tensor b x, y ig N b Tr[ S x, y S y, x] 1

13 From ontour to retrded olriztion tensor ontour x x x, y x y0 x, y x, 0 y, x, y b ig N b Tr[ S, x, y S, y, x] 1

14 Contributions to retrded olriztion tensor in N= SYMP ig d k b N b Tr[ S k S sym S sym S k] For every loo nd tdole there re nlogil ormuls 1

15 Hrd Loo Aroximtion d λ Wvelength o qusi-rtile is muh bigger thn inter-rtile distne in the lsm: d 15

16 Hrd Loo Aroximtion The only dimensionl rmeter in ree ultrreltivisti equilibrium lsm is temerture T. 1 ~ d ~ T ~ 1 ~ d 1 ~ k wve vetor o olletive mode COLLECTIVE MODES: momentum o lsm onstituent k 16

17 Polriztion tensor d k [ k k i b k g N b E k 0 g k ] k n 8n 6n g s the sme struture s in QED nd QCD symmetri k k trnsversl k k 0 Guge indeendene! 17

18 0 ] [ i k k k g k k k E d N g k b b Polriztion tensor 6 8 s g n n n Eet o SUSY: vuum ontribution vnishes the oeiients in ront o the distribution untions re the numbers o degrees o reedom q q g QGP n n N N n 18

19 0 ˆ i k E d N g k ij b ij b The ermion sel-energy hs the sme struture or the N= SYM, SUSY QED nd usul QED lsm. 0 ˆ i k E d e k e QED Fermion sel-energy 6 8 s g n n n 19

20 Slr sel-energy Slr sel-energy: P AB AB b k g N b E n 8n 6n indeendent o k vnishes in the vuum limit g d s 0

21 1 1 HL HL HL A HL A A i i D D DΨ Ψ i F F L L L L y y x x y d x L Sel-energy onstrins the orm o eetive tion ], [, y x S y x Hrd loo eetive tion 1

22 Struture o eh sel-energy is unique HL x F D x F E d N g x b b A L HL x D x E d N g x b i b i L HL x x E d N g x A A L The struture o eh term o the eetive tion ers to be unique From eetive tion to sel-energies

23 Guge bosons olletive modes Disersion eqution det[ k g k k k] 0 Solutions: k k, k The struture o k oinides with the gluon olriztion tensor o QCD lsm suh s o QED nd SUSY QED lsm The setrum o olletive exittions o guge bosons in N= suer Yng-Mills, QCD, QED nd SUSY QED lsm is the sme. There is whole vriety o ossible olletive exittions, in rtiulr there re unstble modes.

24 Fermion olletive modes The struture o ermion sel-energy is suh s o qurk sel-energy in QCD lsm is suh s o QED nd SUSY QED lsm There re identil setr o olletive exittions o ermions in ll systems. No unstble modes ound!

25 Slr olletive modes The slr sel-energy is indeendent o momentum. It is negtive nd rel. P m e m e is the eetive slr mss The solution o disersion eqution: E m e 5

26 Collisionl hrteristis 6

27 Elementry roesses S. C. Huot, S. Jeon, nd G. D. Moore, Phys. Rev. Lett. 98,

28 Trnsort oeiients Collisionl roesses trnsort roerties o ultrreltivisti lsm Temerture is the only dimensionl rmeter. T ln g ~ 1 g S. C. Huot, S. Jeon, nd G. D. Moore, Phys. Rev. Lett. 98,

29 Energy loss nd momentum brodening re not onstrined by dimensionl rguments de dx ~ T, ET, E, qˆ ~ T, ET, E T, E, deend on seii sttering roess under onsidertion 9

30 Cross setions o binry intertions in SUSY QED 0

31 Energy loss nd momentum brodening in SUSY QED lsm A seletron is trversing n equilibrium hoton gs. M e de dx e T T E ET e T 5 qˆ e 1 T 5 T E ET e 1 T 1

32 Comrison with Coulomb-like intertion Energy loss or ontt intertion de dx e T 5 Energy loss or Coulomb-like intertion de dx e E T ln et E. Brten nd M. H. Thom, Phys. Rev. D,

33 energy hnge in single ollision ross setion density inverse men th energy loss Energy loss E 1 de dx ~ 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 Dierent intertions led to the sme energy loss!

34 Conlusions The olletive modes o N= suer Yng-Mills lsm re the sme s those o QGP. There re no unstble ermion modes. The strutures o sel-energies er to be unique. The trnsort hrteristis o SUSY lsm re similr to those o QGP. Both systems re very similr to eh other in the wek ouling regime!