Evaporating Black Hole and Partial Deconfinement Masanori Hanada - PowerPoint PPT Presentation

Evaporating Black Hole and Partial Deconfinement Masanori Hanada University of Southampton 28 Dec 2018 @ YITP , Kyoto

Holographic Principle Black Hole Non-gravitational systems Quantum gravity ‘Equivalent’ Matrix Model Super Yang-Mills SYK ….

Holographic Principle Black Hole Non-gravitational systems Quantum gravity ‘Equivalent’ Matrix Model Super Yang-Mills SYK …. BH

Our world with gravity is secretly non-gravitational.

We want to study it, to learn about quantum gravity. Our world with gravity is secretly non-gravitational.

Goal of Holography Program Solve it. And learn about it. Quark-gluon plasma Black hole CMB ? LHC ALICE Gauge theory ～ QCD Formation of quark-gluon plasma Formation of black hole Energy Mass of black hole “Finite-N, finite-coupling e ff ects” Corrections to Einstein gravity

QCD string force inside atoms q 3 SU(3) gauge theory A μ 32 3 colors q 1 A μ 11 A μ 12 A μ 13 q 2 q 2 A μ 21 A μ 22 A μ 23 A μ 13 q 3 A μ 31 A μ 32 A μ 33 gauge field A μ 12 quark (gluon) q 1

Supersymmetric QCD Gauge Theory string force inside atoms SU(N) gauge theory SU(3) gauge theory 3 colors N colors q 1 A μ 11 A μ 12 A μ 13 A μ 11….. A μ 1N q 2 A μ 21 A μ 22 A μ 23 ………….. q 3 A μ 31 A μ 32 A μ 33 A μ N1 ….. A μ NN gauge field quark (gluon) Ψ 11….. Ψ 1N ………….. Ψ N1….. Ψ NN

(p+1)-d maximal super Yang-Mills = black p-brane (Itzhaki-Maldacena-Sonnenschein-Yankielowicz, 1998) black hole (p=0) black string (p=1) energy = BH mass Temperature Monte Carlo String/M-theory Collaboration, 2017 Catterall-Jha-Schaich-Wiseman, 2017

• Only special theories (maximally supersymmetric etc) describe gravity/string theory.

• Only special theories (maximally supersymmetric etc) describe gravity/string theory. weakly coupled string/gravity.

• Only special theories (maximally supersymmetric etc) describe gravity/string theory. weakly coupled string/gravity. • Various theories, including QCD, describe some (not necessarily weakly coupled) string theory.

• Only special theories (maximally supersymmetric etc) describe gravity/string theory. weakly coupled string/gravity. • Various theories, including QCD, describe some (not necessarily weakly coupled) string theory. • Some ‘stringy’ features can be universal.

universal feature?

Black Hole in AdS 5 × S 5 = 4d N=4 SYM on S 3 Large BH E ~ N 2 T 4 ‘five dimensional’ — S 5 is filled microcanonical ensemble (E fix) ‘ten dimensional’ Small BH — localized along S 5 E ~ N 2 T − 7 Hagedorn String

Graviton gas Hagedorn String Large BH E ~ N 2 T 4 Small BH E ~ N 2 T − 7

Black Hole in AdS 5 × S 5 = 4d N=4 SYM on S 3 Large BH E ~ N 2 T 4 ‘five dimensional’ — S 5 is filled microcanonical ensemble (E fix) ‘ten dimensional’ Small BH — localized along S 5 E ~ N 2 T − 7 Hagedorn String

Black Hole in AdS 5 × S 5 = 4d N=4 SYM on S 3 Large BH E ~ N 2 T 4 ‘five dimensional’ — S 5 is filled canonical ensemble (T fix) ‘ten dimensional’ Small BH — localized along S 5 E ~ N 2 T − 7 Hagedorn String

strongly coupled water/ice 4d SYM VERY DIFFERENT How can we explain such di ff erence?

D-brane bound state and Gauge Theory X 22 X 12 X M = X 23 X 11 X 13 X 33 (X 1ii ,X 2ii ,…,X 6ii ) location of i-th D-brane X Mij : open strings connecting i-th and j-th D-branes. large value → a lot of strings are excited (Witten, 1994)

N N diagonal elements = particles (D-branes) off-diagonal elements = open strings (Witten, 1994) black hole = bound state of D-branes and strings

strongly coupled water/ice 4d SYM VERY DIFFERENT separation in color d.o.f separation in space (MH-Malts, 2016) partially deconfine

N BH N BH N N BH D-branes form the bound state U(N BH ) is deconfined — ‘partial deconfinement’ Can explain E ~ N 2 T − 7 for 4d SYM, N 3/2 T − 8 for ABJM (String Theory → 10d) (M-Theory → 11d) (MH-Maltz, 2016)

Why can negative specific heat appear? N/2 N N T~E/N 2 T’~E’/[2 × (N/2) 2 ] T’>T if E’ > E/2

Why can negative specific heat appear? N BH N BH N T ～ E BH /(N BH ) 2 (more analyses later, or during coffee breaks)

Ant trail/black hole correspondence MH-Ishiki-Watanabe, arXiv:1812.05494 [hep-th]

M-theory (Witten) AdS/CFT (Maldacena)

Ant ‘trail’ is called 行列 in Japanese. ‘Matrix’ is called 行列 in Japanese. Gauge/gravity duality says BH is matrix. black hole = ant trail?

Black hole = D-brane bound by open strings N BH D-branes Ant trail = ants bound by pheromone N trail ants

Black hole = D-brane bound by open strings N BH open strings try to capture N BH D-branes the other D-brane Ant trail = ants bound by pheromone pheromone strength = p × N trail p: pheromone from each ant N trail ants

T James > T others

T James > T others p James > p others

T James > T others p James > p others T ～ p

Black hole = D-brane bound by open strings N BH open strings try to capture N BH D-branes the other D-brane high T ～ each mode is excited more ～ stronger pheromone from each ant Ant trail = ants bound by pheromone pheromone strength = p × N trail p: pheromone from each ant N trail ants

The ant equation = 0 stringy term Natural large-N limit: (many-ant limit)

The ant equation = 0 stringy term N trail /N N trail /N N trail /N

x = N trail /N p ~ T

x = N trail /N Unstable trail ~ “small BH” p ~ T

x = N trail /N stronger and stronger pheromone attract more and more ants dx/dt > 0 weaker and weaker pheromone attract less and less ants p ~ T dx/dt < 0

larger p → smaller N trail is enough for x = N trail /N large p × N trail smaller p → larger N trail is needed for large p × N trail p ~ T

N BH = N 0 < N BH < N N BH = 0 N BH D-branes form the bound state U(N BH ) is deconfined — ‘partial deconfinement’

strongly coupled 4d SYM

strongly coupled weakly coupled 4d SYM 4d SYM

strongly coupled weakly coupled 4d SYM 4d SYM

strongly coupled weakly coupled 4d SYM 4d SYM QCD at physical quark mass QCD at large quark mass

strongly coupled weakly coupled 4d SYM 4d SYM QCD at physical quark mass QCD at large quark mass QCD at μ =0 QCD at finite μ ?

Testing the partial deconfinement Cotler-MH-Ishiki-Watanabe, in preparation

• ‘Polyakov loop’ is a useful order parameter. • Phase distribution: confined phase deconfined phase P=0 P ≠ 0 ‘partially’ deconfined ‘completely’ deconfined

−π π −π π −π π It follows from ‘partial deconfinement’ picture.

N BH N BH N N BH Suppose the same result is obtained from them. N BH

D-branes are emitted N BH beyond here T

D-branes are emitted N BH beyond here SU(M) M < N T In SU(M) theory, D-branes are emitted beyond here

D-branes are emitted N BH beyond here SU(M) M < N T In SU(M) theory, D-branes are emitted beyond here ‘Deconfined parts’ behave the same way

D-branes are emitted beyond here N BH T

D-branes are emitted beyond here N BH SU(M) M < N T In SU(M) theory, D-branes are emitted beyond here

D-branes are emitted beyond here N BH SU(M) M < N T In SU(M) theory, D-branes are emitted beyond here ‘Deconfined parts’ behave the same way

−π π −π π Does it actually hold?

Gross-Witten-Wadia transition separates completely and partially deconfined phases. It does hold in various examples.

T 2 < T 1 not tested yet It does hold in various examples.

Finite density QCD for Hawking Evaporation?

Conjectured QCD phase diagram (from Wikipedia)

Conjectured QCD phase diagram (from Wikipedia)

• ‘Evaporating black hole’ should be there. disclaimer: ‘Gravity dual’ can be very stringy. • What would be the experimental signal? • ‘Applied holography’ should be a good tool.

Conclusion • Ants are smart. They know many things about black hole. • ‘Partial deconfinement’ and ‘Schwarzschild Black Hole’ are rather generic in gauge theories. • ‘Hawking evaporation’ in the heavy ion collision? • It is important to study gauge theory, in order to understand quantum gravity. • Are we smarter than ants?

x = N trail /N = 0 don’t want to be a lone ant

x = N trail /N = 0 don’t want to be a lone ant

+ ε x = N trail /N = 0 don’t want to be a lone ant

Backup Slides

10d Schwarzschild from 4d SYM via Partial Deconfinement M.H., Maltz, 2016

Heuristic Gauge Theory ‘Derivation’ (1) • Take radius of S 3 to be 1. • At strong coupling, the interaction term λ =g YM2 N (N/ λ )*Tr[X I ,X J ] 2 is dominant. • Eigenvalues of Y = λ -1/4 X are O(1) because the interaction is simply N*Tr[Y I ,Y J ] 2 . • Hence eigenvalues of X are O( λ 1/4 ).