Gauge/Gravity Duality

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Gauge/Gravity Duality
Big picture slides Key computations - board
TODAY Introduction Strings Branes
AdS/CFT Correspondence QCD-like dynamics lecture
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Prof Nick Evans
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Resources
D-branes Clifford Johnson
The classic review of the AdS/CFT Correspondence
is Large N field theories, string theory and
gravity.Ofer Aharony, Steven S. Gubser, Juan
Maldacena, Hirosi Ooguri, Yaron Oz.
Phys.Rept.323183-386,2000, hep-th/9905111 A
review of holographic quark and meson physics
is Mesons in Gauge/Gravity Duals - A
Review.Johanna Erdmenger, Nick Evans, Ingo
Kirsch, Ed Threlfall Eur.Phys.J.A3581-133,2008,
arXiv0711.4467 hep-th Transport properties of
gluon plasma Viscosity, Black Holes, and Quantum
Field Theory.Dam T. Son, Andrei O. Starinets.
Ann.Rev.Nucl.Part.Sci.5795-118,2007.
arXiv0704.0240 hep-th These slides can be
found at www.hep.phys.soton.ac.uk/evan
s/GaugeGravity/
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0 Introduction

• String theory was originally an attempt to
  describe mesons
• QCD took over
• String Theory became a quantum theory of gravity
  a TOE
• The AdS/CFT Correspondence has re-united them
• there are now positive links back to QCD
• new pictures of confinement
• new understanding of mass
  generation
• new ideas on hadronization
• novel descriptions of heavy
  ion physics

Smolin Woit are wrong!
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Quarks come in 3 colours 8 gluons mediate the
force
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Hadronization in even electron positron
collisions is very messy and uncomputable from
first principles as for heavy ion collisions.
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Chiral Lagrangian description of pions
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Stringy Hints Regge Trajectories
String theory was originally proposed to explain
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Stringy Hints tHooft says Large N
At large N perturbation theory simplifies and
restricts to planar diagrams Dense gluons -gt a
string world sheet? Quark production hence
string breaking is forbidden at large N
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N
c
N N
c
f
The expansion parameter is
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Waves with no energy flux off the end of a string
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A consistent theory of photons and gravitons? The
TOE era!
Actually a negative world-sheet Cosmological
Constant leaves the un-wavy string as a tachyon.
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Super-Strings
m
To make a consistent theory add fermion partners
to the X living on the string world-sheet
Only anomaly free in 10d
Extra world sheet waves
Same chirality fermions or opposite?
The dilaton vev turns out to be the string
coupling constant
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The links to QCD seem utterly lost until
HOW SHOULD YOU THINK ABOUT THIS? Imagine taking a
field theory and mixing up the equations for
motion in x and RG flow in energy scale into a 5d
theory if the gauge theory is strongly coupled
we dont know these mixed equations they turn
out to be the EoM of strings in AdS!
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Another view
Curved extra dimensions generate a Kaluza Klein
tower
Here the glueballs of the gauge theory are this
tower (at large N an infinite number are
stable).. The spectrum matches the KK tower of an
AdS radial direction
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1/2 The World of Branes
T- Duality in String Theory
Closed strings on a compact space generate two
sets of integer spaced mass states
There is a symmetry between spectra on two
different radii.
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D-branes
Only closed strings see the new direction not
open strings
Electromagnetic particles live on a sub-space or
brane
Dirichlet boundary conditions
Gravitons live in a higher dimension bulk
The extra scalar measures the position of a
dynamical brane in the bulk.
Including multiple D-branes in the space provides
flavour indices for the string ends points. U(1)
-gt U(N) gauge symmetries
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Dirac-Born-Infeld Low Energy Effective Action
Determined by space-time symmetries.
cf a point particle (0-brane)

cf a 1-brane (string)

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Brane Induced Metrics
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1 AdS/CFT Correspondence
All fields in adjoint representation
b 0 - this N4 theory has no running coupling
its conformal!!
The space-time symmetries are boosted to SO(2,4)
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Scalar Moduli Space
SO(6) global symmetry on 6 scalars fermions
transform as 4 of SO(6) due to
Potential
Provided we pick the same generator the 6 scalar
vevs can be any value physically inequivalent
vacua
N
Generically U(N) -gt U(1)
As we decouple string modes we must leave finite
values for vevs.
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Remember the scalar vevs describe the position of
the D3s in the bulk geometry.
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AdS x S
5
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Symmetries of the Geometry
The five sphere isometries are SO(6)
The AdS space has an SO(2,4) isometry group
same moduli space
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Duality?
Note with a -gt 0 Newtons constant has gone to
zero in the gauge theory and the GR theory is
completely disconnected
Gravity approximate strings only at large g N
s
Gravity is only weakly coupled for small g
s
Were at large tHooft coupling in gauge theory
Maldacena are these two copies of the same
physics?
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Extra 5th dimension?
Different u is looking at gauge theory at
different RG scale.. . red shift in the black
hole geometry
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Kim, Romans, van Nieuwenhuizen 1985 Had
computed the sugra spectrum on AdS5xS5 All sugra
states match duality conjecture (but do not give
full operator spectrum string states important
too!)
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The latter is the dilaton - also dual to the
gauge coupling g g
s
YM
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Glueballs
The N4 theory is conformal and so doesnt have
bound states
A simple cure is to compactify the 3d space in
which the N4 theory lives to introduce a scale
and break conformal invariance.. Lets just do
the case where the 31d space becomes a 3-torus
with all radii equal.
We can now investigate the glueball spectrum
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