Recent developments in AdSCFT correspondence

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Recent developments in AdS/CFT correspondence

• Kostya Zarembo
• École Normale Supérieure
• Uppsala U.

Rencontres de Moriond, La Thuile, 10.03.2008
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• Yang-Mills fields closed strings
• rings of glue

or maybe
Polyakov80
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Planar diagrams and strings
Large-N limit
t Hooft74
time
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Conceptual problems

• Closed strings describe gravity. What is graviton
  in YM?
• String theory is only consistent in ten
  dimensions.
• How does the string remember that it is made of
  gluons?

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Bound states in QFT (mesons, glueballs)
String states
Local operators
String states

• Resolves many puzzles of putative large-N string
• graviton is not a massless glueball, but is the
  dual of the energy-momentum tensor Tµ?
• extra dimensions are geometric images of the
  energy scale and of global symmetries
• sum rules are automatic

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AdS/CFT correspondence
Yang-Mills theory with N4 supersymmetry
Maldacena97 Gubser,Klebanov,Polyakov98 Witten98
Exact equivalence
String theory on AdS5xS5 background
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Anti-de-Sitter space (AdS5)
z
5D bulk
strings
0
gauge fields
4D boundary
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AdS/CFT correspondence
Maldacena97
Gubser,Klebanov,Polyakov98 Witten98
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Strong-weak coupling interpolation
?
0
SYM perturbation theory
String perturbation theory
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Circular Wilson loop (exact)
Erickson,Semenoff,Zarembo00 Drukker,Gross00 Pest
un07
Minimal area law in AdS5
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Correlation functions
Dilatation operator
matrix of anomalous dimensions
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Local operators and spin chains
j
i
i
j
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One loop planar mixing matrix
Minahan,Z.02
Heisenberg Hamiltonian
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The spectrum
Ground state
Excited states (magnons)
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periodicity of wave function
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Bethe equations for Heisenberg model
Rapidity
Bethe31
Anomalous dimension
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Full asymptotic BA
Beisert,Staudacher05
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Wrapping/finite size effects
Ambjørn,Janik,Kristjansen05
Weak coupling
wrapping order
captured by ABA
Beisert,Kristjansen,Staudacher03
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Large-spin twist-2 operators
where
Beisert,Eden,Staudacher06
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Weak coupling
Beisert,Eden,Staudacher06
Confirmed by explicit four-loop calculations in
SYM
Bern,Czakon,Dixon,Kosower,Smirnov06
Cachazo,Spradlin,Volovich06
Strong coupling
Basso,Korchemsky,Kotanski07
Confirmed by explicit two-loop calculations in
string theory
Roiban,Tseytlin07 Klose,Minahan,McLoughlin,Z.07
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Conclusions

• Large-N SYM is a solvable (and to certain degree
  solved) 4d theory. The solution is not simple!
• Finite-size/wrapping effects (Asymptotic Bethe
  Ansatz gt Thermodynamic Bethe Ansatz?)
• String theory ltgt Yang-Mills ltgt spin chain
• How does it work in detail?
• What can we learn from solving AdS/CFT exactly?