Obiettivo 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 FieldTheories 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. Campo scientifico natural sciencesmathematicspure mathematicsmathematical analysisfunctional equationsnatural sciencesphysical sciencestheoretical physicsparticle physicsnatural sciencescomputer and information sciencescomputational sciencenatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicsapplied mathematicsmathematical physicsconformal field theory Programma(i) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Argomento(i) ERC-AG-PE2 - ERC Advanced Grant - Fundamental constituents of matter Invito a presentare proposte ERC-2012-ADG_20120216 Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-AG - ERC Advanced Grant Istituzione ospitante CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contributo UE € 1 456 140,00 Indirizzo RUE MICHEL ANGE 3 75794 Paris Francia Mostra sulla mappa Regione Ile-de-France Ile-de-France Paris Tipo di attività Research Organisations Ricercatore principale Vladimir Kazakov (Prof.) Contatto amministrativo Louis Avigdor (Mr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Francia Contributo UE € 1 456 140,00 Indirizzo RUE MICHEL ANGE 3 75794 Paris Mostra sulla mappa Regione Ile-de-France Ile-de-France Paris Tipo di attività Research Organisations Ricercatore principale Vladimir Kazakov (Prof.) Contatto amministrativo Louis Avigdor (Mr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato