Studying the strongly coupled N4 plasma using Ad

Studying the strongly coupled N=4 plasma using Ad. S/CFT Amos Yarom, Munich Together with S. Gubser and S. Pufu

Calculating the stress-energy tensor T FT Ad. S/C J. >> 1 na ace Mald N >> 1

Calculating the stress-energy tensor • Anti-de-Sitter space. • Strings in Anti-de-Sitter space. • The energy momentum tensor via Ad. S/CFT. • Results.

Flat space 2 2++c 2 =2 c= 2 dx dx 22+c dz 2 2 dz+2 dw 2 - dt 2 dsds dy + 2 dy y ds 2 x cx y cy z cz dz 2 z dy 2 dx 2 x

5 d Anti de-Sitter space ds 2 =L 2 z-2 (dz 2+dx 2+dy 2+dw 2 - dt 2) 0 + z

Ad. S 5 black hole 2 dx 2+dw 2 - (1 -(z/z )4) dt 2) ds 2 =L 2 z-2 (dz 2/(1 -(z/z +dy ds 2 =0)g 4)+dx dx 0 0 z

Strings in Ad. S ds 2 = g dx dx ______ 1 2 d d SNG= ___ s √g ( X) 0 2 X ( ) ( , ) z 0 z

N=4 SYM plasma via Ad. S/CFT Ad. S 5 Ad. S/CFT Vacuum Empty Ad. S 5 L 4/ ’ 2 L 3/2 G 5 na ldace J. Ma g. YM 2 N N 2 J. Maldacena hep-th/9711200

N=4 SYM plasma via Ad. S/CFT Ad. S 5 CFT Empty Ad. S 5 Ad. S BH 5 Thermal Vacuum state L 4/ ’ 2 g. YM 2 N L 3/2 G 5 N 2 Horizon radius Temperature J. E. Maldacena Witten hep-th/9802150 hep-th/9711200 T>0

Static ‘quarks’ using Ad. S/CFT 0 Ad. S 5 ? CFT T Endpoint. Aof d. S/CF Massive an open particle string on the na boundary ldace J. Maldacena hep-th/9803002 z 0 z SNG =0 X

Moving ‘quarks’ using Ad. S/CFT 0 ? Ad. S 5 CFT Endpoint of an open string on the boundary Massive particle J. Maldacena hep-th/9803002 z 0 z SNG =0 X

Moving ‘quarks’ using Ad. S/CFT 0 Ad. S 5 CFT Endpoint of an open string on the boundary Massive particle J. Maldacena hep-th/9803002 z 0 z SNG =0 X

Extracting the stress-energy tensor using Ad. S/CFT 0 Ad. S 5 CFT gmn|b <Tmn> E. Witten hep-th/9802150 z

Extracting the stress-energy tensor using Ad. S/CFT 0 Ad. S 5 CFT gmn|b <Tmn> E. Witten hep-th/9802150 z ds 2 = g dx dx g = g. Ad. S-BH+h Ad. S black hole Metric fluctuations

The energy momentum tensor (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022) 0 z g=g. Ad. S+ h

Energy density for v=3/4 (Gubser, Pufu, AY, Ar. Xiv: 0706. 0213, Chesler, Yaffe, Ar. Xiv: 0706. 0368) Over energy Under energy

v=0. 75 v=0. 58 v=0. 25

Small momentum approximations (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022)

Small momentum approximations (Gubser, Pufu, AY, Ar. Xiv: 0706. 0213) 1 -3 v 2 < 0 (supersonic) 1 -3 v 2 > 0 (subsonic)

Small momentum approximations (Gubser, Pufu, AY, Ar. Xiv: 0706. 0213)

Small momentum approximations (Gubser, Pufu, AY, Ar. Xiv: 0706. 0213) s=1/3 cs 2=1/3

Energy density for v=3/4

0

v=0. 75 v=0. 58 v=0. 25

Large momentum approximations (Gubser, Pufu hep-th: 0703090 AY, hep-th: 0703095)

Large momentum approximations (Gubser, Pufu hep-th: 0703090 AY, hep-th: 0703095)

The Poynting vector (Gubser, Pufu, AY, Ar. Xiv: 0706. 4307) S 1 V=0. 25 V=0. 58 V=0. 75 S?

Small momentum asymptotics (Gubser, Pufu, AY, Ar. Xiv: 0706. 4307) Sound Waves ?

Small momentum asymptotics (Gubser, Pufu, AY, Ar. Xiv: 0706. 4307)

The poynting vector (Gubser, Pufu, AY, Ar. Xiv: 0706. 4307) S 1 V=0. 25 V=0. 58 V=0. 75 S?

Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022, Gubser, Pufu, AY, Ar. Xiv: 0706. 0213, 0706. 4307)

Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022, Gubser, Pufu, AY, Ar. Xiv: 0706. 0213, 0706. 4307) 0 F (Herzog, Karch, Kovtun, Kozcaz, Yaffe, hep-th: 0605158, Gubser, hep-th: 0605182) z 0 z

Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022, Gubser, Pufu, AY, Ar. Xiv: 0706. 0213, 0706. 4307)

Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022, Gubser, Pufu, AY, Ar. Xiv: 0706. 0213, 0706. 4307) S 1

Summary • Ad. S/CFT enables us to obtain the energy momentum tensor of the plasma at all scales. • A sonic boom and wake exist. • The ratio of energy going into sound to energy going into the wake is 1+v 2: -1.

The energy momentum tensor Cylindrical Gauge symmetry choice Vector modes Tensor

The energy momentum tensor Tensor modes Vector modes + first order constraint

The energy momentum tensor Tensor modes Vector modes Scalar modes + first order constraint + 3 first order constraints

Large momentum approximations

Large momentum approximations