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Origins of integrability in AdS/CFT correspondence

Objective

Fundamental interactions in nature are well described by quantum gauge fields in 4 space-time dimensions (4d). When the strength of gauge interaction is weak the Feynman perturbation techniques are very efficient for the description of most of the experimentally observable consequences of the Standard model and for the study of high energy processes in QCD.
But in the intermediate and strong coupling regime, such as the relatively small energies in QCD, the perturbation theory fails leaving us with no reliable analytic methods (except the Monte-Carlo simulation). The project aims at working out new analytic and computational methods for strongly coupled gauge theories in 4d. We will employ for that two important discoveries: 1) the gauge-string duality (AdS/CFT correspondence) relating certain strongly coupled gauge Conformal Field
Theories to the weakly coupled string theories on Anty-deSitter space; 2) the solvability, or integrability of maximally supersymmetric (N=4) 4d super Yang-Mills (SYM) theory in multicolor limit. Integrability made possible pioneering exact numerical and analytic results in the N=4 multicolor SYM at any coupling, effectively summing up all 4d Feynman diagrams. Recently, we conjectured a system of functional equations - the AdS/CFT Y-system – for the exact spectrum of anomalous dimensions of all local operators in N=4 SYM. The conjecture has passed all available checks. My project is aimed at the understanding of origins of this, still mysterious integrability. Deriving the AdS/CFT Y-system from the first principles on both sides of gauge-string duality should provide a long-awaited proof of the AdS/CFT correspondence itself. I plan to use the Y-system to study the systematic weak and strong coupling expansions and the so called BFKL limit, as well as for calculation of multi-point correlation functions of N=4 SYM. We hope on new insights into the strong coupling dynamics of less supersymmetric gauge theories and of QCD.

Field of science

  • /natural sciences/physical sciences/string theory
  • /natural sciences/mathematics/pure mathematics/mathematical analysis/functional equations

Call for proposal

ERC-2012-ADG_20120216
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant

Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Address
Rue Michel Ange 3
75794 Paris
France
Activity type
Research Organisations
EU contribution
€ 1 456 140
Principal investigator
Vladimir Kazakov (Prof.)
Administrative Contact
Louis Avigdor (Mr.)

Beneficiaries (1)

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France
EU contribution
€ 1 456 140
Address
Rue Michel Ange 3
75794 Paris
Activity type
Research Organisations
Principal investigator
Vladimir Kazakov (Prof.)
Administrative Contact
Louis Avigdor (Mr.)