Date post: | 18-Jan-2018 |
Category: |
Documents |
Upload: | collin-atkins |
View: | 216 times |
Download: | 0 times |
Integrability for the Full Spectrum of Planar AdS/CFT Nikolay GromovDESY/HU/PNPIV.Kazakov and P.Vieira
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
N=4 Supersymmetric Yang-Mills Theory
The action:
Field content:
YM: Local operators and spin chains
- Dilatation operator – integrable Hamiltonian
The spectrumGround state:
Excited states (magnons):
periodicity condition:
momentumscattering phase shifts
periodicity of wave function
©Zarembo
7
2) Get eigenvalues
1) Solve polynomial equation
YM: One-loop- Integrable Hamiltonian
LepatovFaddeev, KorchemskyMinahan , Zarembo
8
Numerical Solution
Till Bargheer, Niklas Beisert, N. G.
String theory
(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
x
String tension `t Hooft coupling
String coupling Number of colors
AdS/CFT Duality
Summetry:
Beisert, Staudacher;Beisert,Eden,Staudacher
Bethe equations
Vacuum
I.e. from the asymptotical spectrum (R=\infty) we can compute the Ground state energy for ANY finite volume!
SO(4)
Symmetry:
Анзац Бетэ:Zamolodchikov x2Faddeev, Reshetikhin
Ground state from ABAThe typical configuration of roots
isWe define:
Saddle point equation:
Above ground stateDorey, Totteo,Bazhanov
Spectrum of SO(4)
AdS/CFT GeneralizationN.G., Kazakov, Vieira
Large L limit
Use Hirota equation:
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!
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
CP3xAdS4 / N=6 Chern-Simons
N.G., Kazakov, Vieira
Aharony, Bergman, Jafferis and Maldacena
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