Gravity and strongly coupled field theories

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Gravity and strongly coupled field theories

• J. Maldacena
• Quantum Gravity in the Southern Cone IV

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Field Theory
Gravity theory
Gauge Theories QCD
Quantum Gravity String theory
Use the field theory to learn about gravity Use
the gravity description to learn about the field
theory
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AdS/CFT

• Consider a scale invariant (conformal) field
  theory in 13 dimensions.
• Symmetry group SO(2,4)
• Same as symmetries of 14 dimensional
  Anti-de-Sitter space simplest and most
  symmetric negatively curved spacetime
• Quantum gravity in AdS is the same as a conformal
  field theory on the boundary

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• Review Anti-de-Sitter
• Describe a particular conformal field theory

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Anti-de-Sitter space
ds2 R2 (dx231 dz2) z2
R4
AdS5
Boundary
z
z 0
z infinity
It has constant negative curvature, with a radius
of curvature given by R.
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Anti de Sitter space
Solution of Einsteins equations with negative
cosmological constant.
(
)
De Sitter ? solution with positive cosmological
constant, accelerated expanding


universe
Spatial cross section of AdS hyperbolic space
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Spatial section of AdS Hyperbolic space
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Quantum ChromoDynamics
colors (charges) They interact exchanging
gluons

Chromodynamics (QCD)
Electrodynamics
Gauge group
3 x 3 matrices
Gluons carry color charge, so they interact
among themselves
U(1)
SU(3)
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Most supersymmetric QCD or N4 Super Yang
Mills

Supersymmetry
Ramond Wess, Zumino
Bosons Fermions Gluon
Gluino
Many supersymmetries
B1 F1 B2 F2
Maximum 4 supersymmetries, N 4 Super Yang
Mills
Vector boson spin 1 4
fermions (gluinos) spin 1/2 6 scalars
spin 0

SO(6) symmetry
All NxN matrices, N is the number of colors
Susy might be present in the real world but
spontaneously broken at low energies. We study
this case because it is simpler.
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• This theory is scale invariant
• ( QCD is scale invariant classically but not
  quantum mechanically.)

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Large N and strings
Gluon color and anti-color
Open strings ? mesons Closed strings ?
glueballs

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• Gauge theory with a large number of colors give a
  string theory
• String theory gives rise to a gravity theory

At distances larger than the typical size of the
string
ls
Gravity theory
R

Radius of curvature gtgt string length ?
gravity is a good approximation
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Particle theory gravity theory

Most supersymmetry QCD theory
String theory on
(J.M.)
N magnetic flux through S5
N colors
Radius of curvature
Duality
g2 N is small ? perturbation theory is easy
gravity is bad g2 N is large ? gravity
is good perturbation theory is hard
Strings made with gluons become fundamental
strings.
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• Gravity is a good description when ? gtgt 1
• Free strings are a good description for any ? but
  large N
• At finite N we have an interacting string theory
• Assuming the conjecture to be true, then we get a
  full non perturbative description of gravity with
  AdS asymptotic boundary conditions

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Background independence

• We sum over all geometries that have an AdS
  boundary.
• When N is large, there will be typically one
  geometry that gives the dominant contribution.
• The answer depends on the boundary conditions.
  The field theory has a lagrangian determined by
  the boundary conditions.

.

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Lorentz Symmetry

• Classical AdS has an SO(2,4) symmetry group. This
  symmetry is analogous to Lorentz symmetry for
  flat space. If one takes the curvature radius to
  infinity, it becomes the Poincare group (Lorentz
  translations)
• This symmetry is preserved by the quantization,
  in the sense that the dual field theory has the
  full conformal symmetry.

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We will discuss

• New computational techniques. Integrability
• Black holes and applications of black holes to
  field theory problems.
• Computation of Yang Mills scattering amplitudes
  using AdS.

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Integrability
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Integrability

• Energies of string states in AdS Dimensions of
  operators in gauge theory
• Direct computation in the gauge theory
• Planar diagrams ? spin chains
• We get an integrable system, similar to the
  ones appearing in condensed matter.
• Works nicely in a special, large charge, limit.
• Some exact results were found which show how a
  string emerges as ? goes from zero to infinity.

Berenstein, J.M, Nastase, Minahan, Zarembo,
Staudacher, Beisert, Hernandez, Lopez, Eden.
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High spin operators

• In an ordinary gravity theory we do not have
  light (or massless) fields with spin Sgt2.
• In the gauge theory, at very weak coupling, we
  find a large number of light fields with spins
  S2,3,4,5,
• They should get large masses as we go to strong
  coupling.
• ?-S f(?) LogS for large S
• The function f(?) was computed exactly.
• It is also called the cusp anomalous dimension
  and it also appears in scattering amplitudes

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f(?)
From N. Beiserts strings 2007 talk.
Tests the conjecture for large N but any value of
?
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Black holes
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Black holes in AdS
Thermal configurations in AdS.
Entropy SGRAVITY Area of the
horizon SFIELD THEORY Log
Number of states


Evolution Unitary, no
information loss


(these calculations are easier in the AdS3 case)
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Black holes as models for strongly interacting
fluids.

• A black hole corresponds to a gas (or fluids)
  made of strongly interacting gluons.
• We can compute properties of this fluid using the
  gravity description.
• Shear viscosity ? classical damping of
  fluctuations of the horizon
• Einstein equations in the bulk ? fluid dynamics
  equations from the point of view of the boundary
  theory
• One can compute other quantities like the drag
  force that a fast moving quark will feel when it
  moves through this medium.

Kovtun, Son, Starinets, Policastro
Pufu, Gubser, Bhattacharyya, Lahiri ,
Loganayagam, Minwalla
Liu, Rajagopal, Wiedermann Herzog, Karch,
Kovtun, Kozcaz, Yaffe Casalderrey-Solana,
TeaneyGubser
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Black holes in the Laboratory
QCD ? 5d string theory
High energy collision? produces a black hole
droplet of
deconfined phase
quark gluon plasma .
Black hole? Very low shear viscosity? similar to
what is observed at RHIC the most perfect
fluid
Kovtun, Son, Starinets, Policastro
Very rough model, we do not yet know the precise
string theory
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Gluon scattering amplitudes and soap bubbles in
AdS.

• The problem of computing scattering amplitudes in
  the field theory can be mapped to finding certain
  minimal area surfaces in AdS.
• This can be used to test certain existing
  conjectures for the amplitudes.

Alday J M
Bern Dixon Smirnov
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Planar, color ordered amplitude
Minimal area surface ends on a lightlike contour
given by a sequence of light-like segments
corresponding to the momenta of the gluons.
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Conclusions

• Quantum field theories correspond to quantum
  gravity problems with a boundary.
• This can be used to learn about quantum gravity.
• It can be used to study certain quantum field
  theories

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Future
Field theory

• Theories closer to the theory of strong
  interactions
• Solve large N QCD
• Use it as a model for other interesting strongly
• coupled systems

Gravity

• Quantum gravity in other spacetimes
• Understand cosmological singularities

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Is there a dS/CFT ?
Witten Strominger JM
Asymptotic future
Euclidean conformal field theory
?
De-Sitter
Initial singularity
Partition function of a Euclidean field theory
Wave function of the universe
?g Zg
No explicit example is known! How do we get
emergent time ?
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Gravity dual of a confining field theory with a
mass gap
Gravitational potential in the extra dimension
Graviton is localized in the extra
dimension Massive spin 2 particle in 4 dimension
Extra dimension
4 dimensions
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• Gravity background given by solving the gravity
  equations with certain boundary conditions
• The boundary conditions specify the field theory