integrability for the full spectrum of planar ads/cft nikolay gromov desy/hu/pnpi v.kazakov and...
DESCRIPTION
N=4 Supersymmetric Yang-Mills Theory The action: Field content:TRANSCRIPT
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Integrability for the Full Spectrum of Planar AdS/CFT Nikolay GromovDESY/HU/PNPIV.Kazakov and P.Vieira
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Motivation
Spectrum of an interacting field theory is a funny problem by itself
Some quantities are shared with realistic QCD
We can test string/gauge duality
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N=4 Supersymmetric Yang-Mills Theory
The action:
Field content:
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YM: Local operators and spin chains
- Dilatation operator – integrable Hamiltonian
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The spectrumGround state:
Excited states (magnons):
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periodicity condition:
momentumscattering phase shifts
periodicity of wave function
©Zarembo
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7
2) Get eigenvalues
1) Solve polynomial equation
YM: One-loop- Integrable Hamiltonian
LepatovFaddeev, KorchemskyMinahan , Zarembo
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Numerical Solution
Till Bargheer, Niklas Beisert, N. G.
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String theory
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(type IIB super) string theory in AdS5xS5 x
is dual to a 4 dimensional conformal field theory (N=4 SYM)
Local operators String states
Maldacena
AdS/CFT Duality
Anomalous dimensions Spectrum
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x
String tension `t Hooft coupling
String coupling Number of colors
AdS/CFT Duality
Summetry:
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Beisert, Staudacher;Beisert,Eden,Staudacher
Bethe equations
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Vacuum
I.e. from the asymptotical spectrum (R=\infty) we can compute the Ground state energy for ANY finite volume!
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SO(4)
Symmetry:
Анзац Бетэ:Zamolodchikov x2Faddeev, Reshetikhin
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Ground state from ABAThe typical configuration of roots
isWe define:
Saddle point equation:
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Above ground stateDorey, Totteo,Bazhanov
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Spectrum of SO(4)
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AdS/CFT GeneralizationN.G., Kazakov, Vieira
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Large L limit
Use Hirota equation:
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20
S-matrix
Obeys Yang-Baxter:
Then (see lectures of Faddeev hep-th/9605187 ):
SU(2|2) invariant tensor with 4 fundamental indeses
The eigevalues solves hirota!
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Konishi operator
For weak coupling constant:
The simplest operator
In agreement with perturbation theory!!4-loops!
Kotikov, Lipatov, Rej, Staudacher and VelizhaninSieg, TorrielliJanik, Bojnok, N.G., Kazakov, Vieira
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CP3xAdS4 / N=6 Chern-Simons
N.G., Kazakov, Vieira
Aharony, Bergman, Jafferis and Maldacena
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Conclusions
We can go below BAE nowIntegrability allows to predict
very complicated perturbative calculations
It is possible to compute some quantities for arbitrary coupling
QCD BFKL could be checked