n-point correlators of twist-2 operators in SU(N) Yang-Mills theory to the lowest perturbative order

We compute, to the lowest perturbative order in SU(N) Yang-Mills theory, n-point correlators in the coordinate and momentum representation of the gauge-invariant twist-2 operators with maximal spin along the p+ direction, both in Minkowskian and — by analytic continuation — Euclidean space-time. We also construct the corresponding generating functionals. Remarkably, they have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields.

The Higgs mechanism in nonlocal field theory

We provide an example of nonlocal scalar electrodynamics that allows the same Higgs mechanism so successful in local field theory. The nonlocal action is structured in order to have the same exact solutions and the same equations of motion for perturbations of the local theory, at any perturbative order. Therefore, the perturbative degrees of freedom that propagate in the unstable vacuum are reshuffled when the stable vacuum is replaced in the EoM, but their number does not change at any perturbative order, and their properties are the same like in the usual local theory. Finally, the theory is superrenormalizable or finite at quantum level.

Reggeon field theory and self duality: making ends meet

Motivated by the question of unitarity of Reggeon Field Theory, we use the effective field theory philosophy to find possible Reggeon Field Theory Hamiltonians HRFT. We require that HRFT is self dual, reproduce all known limits (dilute-dense and dilute-dilute) and exhibits all the symmetries of the JIMWLK Hamiltonian. We find a family of Hamiltonians which satisfy all the above requirements. One of these is identical in form to the so called “diamond action” discussed in [67, 68]. However we show by explicit calculation that the so called “diamond condition” is not satisfied beyond leading perturbative order.

Feynman diagrams and rooted maps

The rooted maps theory, a branch of the theory of homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.