Gauge/gravity duality
and applications
Dam Thanh Son (University of Chicago)
Inauguration conference, ICISE, Quy Nhon,Vietnam
Plan
•
•
•
•
QCD, large Nc limit
Gauge/gravity duality
Quark/gluon plasma, viscosity
Applications to condensed matter physics
QCD: nonperturbtive part of
the Standard Model
SU (3) ⇥ SU (2) ⇥ U (1)
|
{z
}
QCD: nonperturbtive part of
the Standard Model
SU (3) ⇥ SU (2) ⇥ U (1)
|
{z
}
electroweak interactions
Glashow-Weinberg-Salam
QCD: nonperturbtive part of
the Standard Model
SU (3) ⇥ SU (2) ⇥ U (1)
|
{z
}
electroweak interactions
Glashow-Weinberg-Salam
strong interactions
QCD: nonperturbtive part of
the Standard Model
SU (3) ⇥ SU (2) ⇥ U (1)
|
{z
}
electroweak interactions
Glashow-Weinberg-Salam
strong interactions
Asymptotic freedom Gross Politzer Wilczek 1972
Asymptotic states are hadrons, not quarks and gluons
’t Hooft large Nc limit
Nc ! 1,
g ! 0,
g 2 Nc = fixed
Only planar diagrams survive
look like string worldsheets
Effective string theory description of large Nc QCD?
I
fat flux tube
vs
elementary string
Gauge gravity duality
•
Maldacena 1997: equivalence
Strongly coupled QFT
in 3+1 dimensions
()
String theory
in 10 dimensions
Complete surprise:
•Different numbers of dimensions
•Role of gravity
g 2 Nc
1
()
Einstein’s gravity
“Holography”
Approaching QCD
•
“Bottom-up” approach: modify the gravitational
background
to
have
confinement
and
chiral
gauge symmetry of the N D8-D8 pairs. The very existence of the compact direction plays
symmetry
a crucial role breaking
in obtaining a holographic understanding of chiral symmetry breaking. The
f
•
•
•
radial coordinate U transverse to the D4-branes is known to be bounded from below due to
the existence of a horizon U ≥ UKK in the supergravity background. As U → UKK , the radius
Erlich, Katz, Son, Stephanov “QCD and a
of the S shrinks to zero. It is found through the study of the DBI action that the D8/D8
holographic model of hadrons” 2005
1
branes merge at some point U = U0 to form a single component of the D8-branes, yielding,
in general, a one-parameter family of solutions (See Fig. 1).∗) On the resultant D8-brane,
Da Rold, Pomarol “χSB from 5D spaces” 2005
only a single factor of U(Nf ) survives as the gauge symmetry. We interpret this mechanism
as a holographic manifestation of the spontaneous breaking of the U(Nf )L × U(Nf )R chiral
“Top-down”
approach: find string theory solutions with
symmetry.
properties of QCD
D8
•
Sakai-Sugimoto model
S
1
D8
S
1
D8
U
U0
U kk
Viscosity of the quark gluon
plasma
•
Very high-temperatures: hadrons melt to quarks
and gluons: quark-gluon plasma
•
•
Goal of RHIC and LHC heavy ion experiments
•
Holography: QGP ~ black hole in AdS space
Surprise of RHIC and LHC: QGP behaves like an
almost ideal fluid
“Prediction” of gaugegravity duality
⌘
~
=
s
4⇡
“Prediction” of gaugegravity duality
viscosity
fluid mechanics
⌘
~
=
s
4⇡
“Prediction” of gaugegravity duality
viscosity
fluid mechanics
⌘
~
=
s
4⇡
entropy per unit volume
thermodynamics
“Prediction” of gaugegravity duality
viscosity
fluid mechanics
quantum mechanics
⌘
~
=
s
4⇡
entropy per unit volume
thermodynamics
v2 (percent)
Recent numerical simulations
15
Viscosity of the QGP
η/s=0.16
Glauber
25
-4
2
pT [GeV]
3
4
-4
η/s=10
25
STAR non-flow corrected (est).
STAR event-plane
1
2
pT [GeV]
η/s=0.08
η/s=0.24
η/s=0.08
3
4
v2 (percent)
1
CGC
0 20
0
v2 (percent)
20
5
η/s=10
STAR non-flow corrected (est.)
STAR event-plane
η/s=0.16
10
15
m Luzum
and Romatschke, arXiv:0804) 15
η/s=0.16
marks:
10
10
Reproduce
main features of the data
5
η/s=0.16
5
Sensitive
to the choice
of initial4 condition
0
0
0
1
2
3
0
pT [GeV]
η/s=0.24
1
η/s is at most a few times !/(4π)
(from
Luzum andand
Romatschke,
arXiv:0804)
Romatschke
Luzum
2
pT [GeV]
3
4
Remarks:
η
= 0.1of±the
0.1(
th) ± 0.08(exp)
Reproduce main features
data
s
Sensitive to the choice of initial condition
Not too far away from 1/4π
η/s is at most a few times !/(4π)
QGP is strongly coupled (sQGP)
G
Applications to condensedmatter physics?
Strongly coupled superconductors
•
Motivation: high-Tc superconductivty
•
Normal phase with nontrivial properties
(“strange
n cuprates: extended
tail metal”)
Optical conductivity from holography: first pass
ene
lden, Lin,
4]
•
Gauge/gravity duality: enables studies of some
• For any z , looks more like graphene than a cuprate.
models of strongly coupled superconductors
N
• Lacking lattice ) Drude peak a delta function.
1.2
1.0
0.8
`
Re s 0.6
0.4
0.2
0.0
0
[Li, Henriksen, Jiang, Hao, Martin, Kim,
Sean Hartnoll
Stormer, Basov ’04]
(Stanford)
1
2
w
`
m
3
Herzog,
Harnoll,
Horowitz
Holographic
supeconductivity
4
M2S
16 / 20
Entanglement entropy
⇢A = trB ⇢tot
A
B
SA =
tr ⇢A ln ⇢A
Entanglement entropy from holography (Ryu-Takanayagi)
Gravity in quantum Hall effect?
•
2 types of quantum Hall effects
•
•
integer QHE (von Klitzing 1980)
fractional QHE (Tsui, Stormer 1982)
n=3
n=2
n=1
IQH
FQH
Excitations in FQH systems
•
•
Ground state degeneracy lifted by interactions
Excitations
•
•
fractionally charged quasiparticles
neutral magneto-rotons
Physics is strongly nonperturbative (cf. QCD)
Useful gravitational dual?
Gravity for QHE
•
The theory of QHE can be formulated to be
frame-independent, like General Relativity
•
A convenient framework: Newton-Cartan’s
geometry
Cartan 1923-1924
Reformulation of Newton’s theory of gravity
Cartan 1923-1924
Reformulation of Newton’s theory of gravity
Cartan 1923-1924
Reformulation of Newton’s theory of gravity
Cartan 1923-1924
Reformulation of Newton’s theory of gravity
Cartan 1923-1924
Reformulation of Newton’s theory of gravity
Cartan 1923-1924
Reformulation of Newton’s theory of gravity
Cartan 1923-1924
Reformulation of Newton’s theory of gravity
t+
v t
gij ,
vi
t
A prediction of NewtonCartan formalism
Hall conductivity at nonzero wavenumber
Ex = E eiqx
y
E
v
xy (q)
xy (0)
v
jy =
x
E
= 1 + C2 (q ) + O(q
2
4 4
)
xy (q)Ex
Carlos Hoyos, DTS 2011
DTS 2013
universal coeff.
1
C2 =
4⌫
1
1, ⌫ =
2p + 1
Magnetoroton as emergent
graviton?
•
•
Haldane: there is a hidden metric in FQH systems
A graviton, made massive by a gravitational Higgs
mechanism S.Golkar, Nguyễn Xuân Dũng, DTS, to appear
(@i uj + @j ui + hij )2
fluid displacement = NG boson (eaten)
magnetoroton = graviton
magnetoroton at q=0 has spin polarization
Conclusion
•
Gauge/gravity duality: connections between
seemingly unrelated systems
•
Black holes in AdS space as rough model of the
strongly coupled QGP
•
•
Maybe useful for condensed matter physics
Fractional quantum Hall systems: a system with
emergent massive graviton?