19/07/2016, 16:20 — 17:00 — Amphitheatre Ea1, North Tower, IST
Pavel Buividovich, Regensburg University

Generalized Series Expansions in Asymptotically Free Large-$N$ Quantum Field Theories

We consider lattice perturbation theory for large-$N$ quantum field theories with unitary $U(N)$ matrices as fundamental degrees of freedom, such as principal chiral models and lattice gauge theories. We argue that a proper treatment of the Jacobian of the transformation which maps $U(N)$ group manifold to a space of Hermitian matrices, which is a necessary ingredient in the construction of perturbative expansions, results in a massive bare propagator. Since the number of planar diagrams grows only exponentially with order, this ensures the absence of any factorial divergences in (bare) lattice perturbation theory. The price to pay is that the perturbative expansion is no longer organized as an expansion in powers of coupling, but rather has a look of generalized series involving, in general, both powers and logs of coupling. I demonstrate the convergence of such expansion on the examples of several large-$N$ models, where results are available either from exact solution or numerical studies with infinite $N$ extrapolations.

See also

R-buividovich.pdf