Paper detail

Glueballs in large-N YM by localization on critical points

By exploiting in large-N YM the change of variables from the gauge connection to the ASD part of its curvature by a non-SUSY version of the Nicolai map, we show that certain twistor Wilson loops supported on a Lagrangian submanifold of twistor space are localized on lattices of surface operators of Z(N) holonomy that form translational invariant sectors labelled by the magnetic charge k=1,2,...,N-1 at a point. The localization is obtained reducing the loop equation in the ASD variables in the holomorphic gauge, regularized by analytic continuation to Minkowski space-time, to a critical equation, by exploiting the invariance of the twistor Wilson loops by deformations for the addition of backtracking arcs ending with cusps on the singular divisor of surface operators. Alternatively localization is obtained contracting the YM measure in the ASD variables on the fixed points of a semigroup that acts on the fiber of the Lagrangian twistor fibration which twistor Wilson loops are supported on and leaves invariant their v.e.v.. The masses squared of the fluctuations of surface operators in the sectors labelled by k, supported on the Lagrangian submanifold analytically continued to Minkowski space-time, form a trajectory linear in k that does not include any massless state. The glueballs propagators in the holomorphic/antiholomorphic sector defined by correlators of a complex combination of the ASD curvature and its adjoint saturate at short distances the logarithms of perturbation theory by a sum of pure poles. In this framework Regge trajectories of higher spins are related to fluctuations of surface operators with pole singularities of any order.