Evaporating Black HoleandPartial Deconfinement
Masanori Hanada
University of Southampton

28 Dec 2018 @ YITP, Kyoto

Holographic Principle
Black Hole
Quantum gravity

Non-gravitational
systems‘Equivalent’Matrix Model
Super Yang-MillsSYK….

Holographic Principle
Black Hole
Quantum gravity

BH

Non-gravitational
systems‘Equivalent’Matrix Model
Super Yang-MillsSYK….

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
plasmaBlack hole

LHC ALICE

CMB ?

Gauge theory 〜 QCD

Formation of quark-gluon plasma

Formation of black hole

EnergyMass of black hole“Finite-N, finite-coupling eﬀects”

Corrections to Einstein gravity

QCD

string force
inside atoms

q3

SU(3) gauge theory

Aμ32

3 colors
Aμ11 Aμ12 Aμ13
Aμ21 Aμ22 Aμ23
Aμ31 Aμ32 Aμ33
gauge field(gluon)

q1q2
q3quark

q2Aμ13Aμ12q1

QCD

string force
inside atoms

SU(3) gauge theory
3 colors

Supersymmetric
Gauge Theory
SU(N) gauge theory
N colorsAμ11 Aμ12 Aμ13
Aμ21 Aμ22 Aμ23
Aμ31 Aμ32 Aμ33

q1q2q3gauge field(gluon)quark

Aμ11…..Aμ1N…………..

AμN1 …..AμNN

Ψ11…..Ψ1N…………..

ΨN1…..ΨNN

(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 (notnecessarily weakly coupled) string theory.

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

• Various theories, including QCD, describe some (notnecessarily weakly coupled) string theory.

• Some ‘stringy’ features can be universal.

universal feature?

Black Hole in AdS5×S5 = 4d N=4 SYM on S3
Large BH
E ~ N2T4‘five dimensional’— S5 is filled
microcanonicalensemble(E fix)Small BH
‘ten dimensional’
E ~ N2T−7 — localized along S5
Hagedorn String

Graviton gas

Small BH
E ~ N2T−7

Hagedorn String

Large BH
E ~ N2T4

Black Hole in AdS5×S5 = 4d N=4 SYM on S3
Large BH
E ~ N2T4‘five dimensional’— S5 is filled
microcanonicalensemble(E fix)Small BH
‘ten dimensional’
E ~ N2T−7 — localized along S5
Hagedorn StringBlack Hole in AdS5×S5 = 4d N=4 SYM on S3
Large BH
E ~ N2T4‘five dimensional’— S5 is filledcanonicalensemble(T fix)Small BH
‘ten dimensional’
E ~ N2T−7 — localized along S5Hagedorn Stringstrongly coupled
4d SYMwater/ice

VERY
DIFFERENT

How can we explainsuch diﬀerence?

D-brane bound state and Gauge Theory
X12

XM =

X22
X23

X11
X13

X33
(X1ii,X2ii,…,X6ii)
location of i-th D-brane
XMij : open strings connecting i-th and j-th D-branes.
large value → a lot of strings are excited(Witten, 1994)

NN
diagonal elements = particles (D-branes)
off-diagonal elements = open strings(Witten, 1994)

black hole = bound state of D-branes and stringsstrongly coupled
4d SYMwater/ice

VERY
DIFFERENT

separation in color d.o.f

separation in space(MH-Malts, 2016)

partially deconfine

NBH
NBH

N
NBH D-branes form the bound state
U(NBH) is deconfined — ‘partial deconfinement’Can explain E ~ N2T−7 for 4d SYM, N3/2T−8 for ABJM(String Theory → 10d)

(M-Theory → 11d)

(MH-Maltz, 2016)

Why can negative specific heat appear?
N/2N
N
T~E/N2T’~E’/[2×(N/2)2]

T’>T if E’ > E/2

Why can negative specific heat appear?
NBH
NBH

NT 〜 EBH/(NBH)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

NBH D-branes

Ant trail = ants bound by pheromone

Ntrail ants

Black hole = D-brane bound by open strings
NBH open strings
try to capture
the other D-brane

NBH D-branes

Ant trail = ants bound by pheromone
pheromone strength = p × Ntrail
p: pheromone from each ant
Ntrail ants

TJames > Tothers

TJames > Tothers
pJames > pothers

TJames > Tothers
pJames > pothers

T〜pBlack hole = D-brane bound by open strings
NBH open strings
try to capture
the other D-brane

NBH D-branes

high T 〜 each mode is excited more〜 stronger pheromone from each ant

Ant trail = ants bound by pheromone
pheromone strength = p × Ntrail
p: pheromone from each ant
Ntrail ants

The ant equation=0
stringy term

Natural large-N limit:(many-ant limit)

The ant equation=0
stringy term
Ntrail/N

Ntrail/N

Ntrail/N

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

p~Tx = Ntrail/Nstronger and stronger pheromone
attract more and more ants

dx/dt > 0weaker and weaker pheromone
attract less and less ants

dx/dt < 0p~T

x = Ntrail/Nlarger p → smaller
Ntrail is enough forlarge p×Ntrail

smaller p → larger
Ntrail is needed forlarge p×Ntrail

p~T

NBH = N

0 < NBH < N
NBH = 0NBH D-branes form the bound state
U(NBH) is deconfined — ‘partial deconfinement’strongly coupled
4d SYMstrongly coupled
4d SYM

weakly coupled
4d SYMstrongly coupled
4d SYM

weakly coupled
4d SYMstrongly coupled
4d SYM

weakly coupled
4d SYM

QCD at large quark mass

QCD at physical quark mass

strongly coupled
4d SYM

weakly coupled
4d SYM

QCD at large quark mass

QCD at physical 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
P=0

deconfined phaseP≠0‘partially’ deconfined‘completely’ deconfined

−π−ππ−ππ

It follows from ‘partial deconfinement’ picture.

πNBHNBHN

NBH
NBH

Suppose the same result
is obtained from them.

NBH

D-branes are emitted
beyond here

T

NBH

D-branes are emitted
beyond here

SU(M)
M<NT
In SU(M) theory,
D-branes are emitted
beyond here

NBH

D-branes are emitted
beyond here

SU(M)
M<NT
In SU(M) theory,
D-branes are emitted
beyond here

‘Deconfined parts’ behave the same way

NBH

D-branes are emitted
beyond here

T

NBH

D-branes are emitted
beyond here

SU(M)
M<N

In SU(M) theory,
D-branes are emittedbeyond hereT

NBH

D-branes are emitted
beyond here

SU(M)
M<NIn SU(M) theory,
D-branes are emitted
beyond hereT‘Deconfined parts’ behave the same way

−π−πππ

Does it actually hold?

Gross-Witten-Wadia transition separates
completely and partially deconfined phases.

It does hold in various examples.

not tested yet

It does hold in various examples.

T2 < T1

Finite density QCD
forHawking 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 tounderstand quantum gravity.

•Are we smarter than ants?

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

+εx = Ntrail/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 S3 to be 1.

•

At strong coupling, the interaction term(N/λ)*Tr[XI,XJ]2 is dominant.

•Eigenvalues of Y = λ-1/4X are O(1)because the interaction is simply N*Tr[YI,YJ]2.

•Hence eigenvalues of X are O(λ1/4).

λ=gYM2NHeuristic Gauge Theory ‘Derivation’ (2)
NBH

XBH

•

When bunch size shrinks to NBH<N, ’t Hooft coupling
effectively becomes λBH=gYM2NBH
λ=gYM2N•Hence eigenvalues of XBH are O(λBH1/4) = O(gYM1/2NBH1/4).
•

EBH〜NBH2(NBH/N)-1/4, SBH〜NBH2•

TBH〜(NBH/N)-1/4

Heuristic Gauge Theory ‘Derivation’ (3)•EBH〜NBH2(NBH/N)-1/4, SBH〜NBH2•

TBH〜(NBH/N)-1/4•

EBH〜N2(NBH/N)7/4〜1/(GN,10TBH7)

NBH

10d Schwarzschild•

SBH〜N2(NBH/N)2〜1/(GN,10TBH8)•The same logic applied to M-theory region of ABJM
gives 11d Schwarzschild, E~1/GN,11T8.

AdS5×S5

T

E〜T4NBHHagedorn

N

E < EminE
How about this?

TBH=THagedorn〜1
EBH〜Smin〜NBH2
when gYM2NBH <<1

Just perturbative SYM.
gYM2NBH <<1

AdS5×S5

T

E〜T4

NBH

Hagedorn

E〜T-7

N

E < EminE

Our argument is not good enoughto capture this jump.

Large BH = ‘Large’ Matrices
Small BH = ‘Small’ Matrices

λ>>1

AdS5×S5T

E〜T4Hagedorn

E〜T-7

E

E〜T4T
Hagedorn

λ<<1(see e.g. Aharony et al 2003)

E