"Yang-Mills theory describes the strong interactions of quarks and gluons to form particles such as the proton. It is widely acknowledged as an important outstanding problem at the frontier of physics with connections to condensed matter, mathematical & computational physics. The large N expansion is a promising method to solve the strongly coupled infrared of the theory and quantitatively test its predictions. The proposal's 1st part concerns bound states in an asymptotically free theory, Spherical QCD. It is relevant to experimentally measured form factors and spectra of b-mesons. The aim is to find the meson spectrum and wave functions by a non-perturbative renormalization of the bound state equation for color-singlet variables in the large-N limit. The 2nd part concerns dynamical matrix-valued gluons in 2d QCD coupled to adjoint scalars (relevant to gluon distribution of proton) and QCD on a cylinder. We transform to open and closed string variables and determine a variational principle for the large N Schwinger-Dyson equations and approximation methods for them. The applicant did his PhD in USA and received the American Physical Society's prestigious Apker Award. From previous research, he has a good physical intuition and special technical skills necessary for this project. It will be done at Utrecht in The Netherlands, supervised by Nobel Laureate G. 't Hooft. The training (including EU RTN networks) and collaboration with European physicists will significantly advance his research career. His original viewpoint, novel techniques and training in USA will contribute to the excellence and competitiveness of European science. On the long term, the applicant will use the expertise and training to pursue an academic research career in India while maintaining collaborative ties with European groups. This will lead to the development of mutually beneficial research cooperation between scientists in Europe and India."
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