Tata Institute of Fundamental Research Black Hole1226 /BH

ND N: Gauge/Gravity correspondenceItzhaki-Maldacena-Sonnenschein-Yankielowicz(1999)p+1 U(N) N Dp

ND N: Gauge/Gravity correspondenceItzhaki-Maldacena-Sonnenschein-Yankielowicz(1999)p+1 U(N) N Dp ?N:

Gauge/Gravity

cf. -: QCD AdS/CMP:

() ()

Gauge/Gravity correspondenceItzhaki-Maldacena-Sonnenschein-Yankielowicz(1999)

Gauge/Gravity

() ()

Gauge/Gravity correspondenceItzhaki-Maldacena-Sonnenschein-Yankielowicz(1999)?

Gauge/Gravity correspondenceItzhaki-Maldacena-Sonnenschein-Yankielowicz(1999) 2dSYM Black hole/Black string (Basu-Mandal-T.M.-Wadia work in progress) BS(BH)

AdS boundaryCFT() (Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)

Introduction and Motivation -gauge/gravity correspondence- -2dSYMBS/BH- -AdS/Fluid-Conclusion and Discussion

Horowitz-Maeda (2001) affine time affine time D particle black string BS ( )affine time) affine time: ()BH/BSGregory-Laflamme (1993)cf. BH

BS (Choptuik et al)horizon(Choptuik et al): horizon: BH/BSGregory-Laflamme (1993)

/BH/BS1/N (Choptuik et al)BSBH/BSGregory-Laflamme (1993)

IIA 1d SYM (Matrix theory) onT-dual 2d U(N) SYM(D1-branes) on: : ND0braneGravityGauge theory(2D SYM)BS/BHSusskind (1998), Aharony, Marsano, Minwalla, Wiseman (2004) + Papadodimas, Raamsdonk (2005)2d SYMBH/BSBH/BSsource

IIA 2d U(N) SYM: ND0braneGravityGauge theory(2D SYM)BS/BHBH/BSsourceNfermion(N D0brane)

BS/BH2dSYM unitary matrix modelNFermionmapFermioninteraction(fermionOK)Unitary matrix model?D0 brane

BS/BHNFermionphase spasedroplet)1Fermion 1/N) NFermion total area1

BS/BHNFermionphase spasedroplet3 staticUniformNon-UniformGapped

BS/BHFermion()S1D0 braneUniformNon-UniformGapped

BS/BHBS/BHD0 braneHorizonUniform black stringNon-uniform BSblack hole

BS/BHBS/BHUBSUBSBHBHUBSNUBSBHUBSNUBSBHBHUBSN FermionUDUDGDGDUDNUDGDUDNUDGDGDUD(UD: uniform, NUD: non-uniform, GD: Gapped)(UBS: uniform BS, NBS: non-uniform BS)bosonic 2dYM

BS/BH2dSYMN fermionN

BS/BHN fermionGapped BS/BHconsistentUniform+Fermion()BH or NUBS(?)

BS/BHHorowitz-Maeda in 2d SYMBHNUBS: (N)phase spacedroplettopologyNUBS

BS/BHHorowitz-Maeda in 2d SYMBHNUBS: (N)phase spacedroplettopologyBH

BS/BHHorowitz-Maeda in 2d SYMBHBSD0phase space

2dSYMN fermionBH/BSSummary 2d SYM Hamiltonian1/N HawkingN

2dSYMN fermionBH/BSSummary SYMBS near extremal BH/BS SYM BH/BSreduction

Introduction and Motivation -gauge/gravity correspondence- -2dSYMBS/BH- -AdS/Fluid-Conclusion and Discussion

BHQ. ?

Q. ? ()BHBH??

: (E, Q, etc) :vector()

: (E, Q, etc) :vector()shear: 4CFT: EM tensorAdS/CFT

AdS/CFT AdS54d CFTboundaryAdS BHThermal CFT (SYM)) AdS5 static black brane4d CFTCFT ?

black brane in AdS5boundarytime-like killing: temperature: Eddington-Finkelstein coordinate(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)

boundarytime-like killing: Eddington-Finkelstein coordinateboost (transverse direction): constant boost parameter: constant: temperatureblack brane in AdS5(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)

boundaryblack brane in AdS5(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)BoundaryBoundaryBrown-York EM tensormetricCFTEM tensorThermal CFTStefan-Boltzmann

AdS(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)CFT1.

AdS(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)CFT1. 2. metric Eddington-Finkelstein coordinatehorizon metric

AdS(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)CFT1. 2. metricBrown-York EM tensorCFTviscosity: Policastro-Son-Starinets

(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)3.horizonentropyi) Temperature Killingsurface gravity boundary ii) Energy Boundary EM tensoriii) Entropy (BHMR+Loganayagam+Mandal+T.M+Reall) Event Horizon

(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)3.

4. (BM+Loganayagam+Nampuri+Trivedi-Wadia) dilaton boundaryflat

(Banerjee-Bhattacharya-B-Dutta-Loganayagam+Surowka) U(1)

(BM+Wadia)

AdS5

(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)

5. RHIC AdS/CMP (Nakamura-Sin, Maeda-Natsuume-Okamura, Kinoshita-Mukohyama-Nakamura-Oda, Haack-Yarom, Maeda-Miyamoto, Hasen-Kraus, Fouxon-Oz, Kanitscheider-Skenderis, Son-Surowka, DHoker-Kraus) AdS/CFT (Policastro-Son-Starinets) viscosity bound? (Myers-Paulos-Sinha) New viscosity bound? (Brigante-Liu-Myers- Shenker-Yaida) 5 GB gravity : GB boundary causality GB gravityviscosity bound?(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)

5. Membrane paradigm Stretched horizon AdSuniversal bulk viscosity universal

Membrane paradigmAdS/CFT (Iqbal-Liu) Membrane paradigmshear viscosityconductivityAdS/CFT

Black hole formationCFT (Bhattacharyya-Minwalla) AdS5 dilaton SmallCFT

(Bhattacharyya-Hubeny-Minwalla-Rangamani 2008)

Gauge/Gravity() BS/BH()2dSYM

CFT

BS/BH2d U(N) SYM

BS/BH2d SYM on 1 bosonic YM on (Mandal-Mahato-T.M.) Wilson loop U2d U(N) SYM1/N

BS/BH(Mandal-Mahato-T.M.) Wilson loop Uproposal2 SYMeffective action2d U(N) SYM1/N

BS/BHproposal2 SYMeffective action() bosonic 2d YM 2dSYM BH/BS2d U(N) SYM

BS/BH1 SYMKabat et alNishimura et al1d YM(Mandal-Mahato-T.M)2d U(N) SYM2d SYM1dYM?BHBSUnknown