1107.4320 (Marco Bochicchio)

Glueballs in large-N YM by localization on critical points    [PDF]

Marco Bochicchio

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.

View original: http://arxiv.org/abs/1107.4320