Sum Of Planar Diagrams Research Articles

D-brane dynamics in thec=1matrix model

Recent work has shown that unstable D-branes in two dimensional string theory are represented by eigenvalues in a dual matrix model. We elaborate on this proposal by showing how to systematically include higher order effects in string perturbation theory. The full closed string state produced by a rolling open string tachyon corresponds to a sum of string amplitudes with any number of boundaries and closed string vertex operators. These contributions are easily extracted from the matrix model. As in the AdS/CFT correspondence, the sum of planar diagrams in the open string theory is directly related to the classical theory in the bulk, i.e. sphere diagrams. We also comment on the description of static D-branes in the matrix model, in terms of a solution representing a deformed Fermi sea.

Planar Diagrams versus Chiral Solitons

It is noted that the sum of planar diagrams in QCD 4 is not a sum of poles, contrary to the literature. Implications for chiral soliton models are discussed

Chiral gauge theories in the 1/ N expansion

We study the large- N limit of various (SU( N) gauge theories with chiral fermion content. Assuming that the leading N → ∞ behavior is given by a sum of planar diagrams, we find that the gauge interactions must fail to confine color in some models. Other models, assuming both a planar diagram limit and confinement, must contain massless composite fermions.

Semiclassical Approach to Planar Diagrams

It is shown, on the basis of an SU(N)-symmetric model, that the large-N quantum theory can be described in terms of the classical equation of motion supplemented by some special boundary conditions. It is then exemplifyied how the appropriate classical solutions determine the sum of planar diagrams.

Non-planar diagrams in the large N limit of U(N) and SU(N) lattice gauge theories

It is shown that the limit as N → ∞ with g2N fixed of the strong coupling expansion for the vacuum expectation values of a U(N) or SU(N) lattice gauge theory is not given by a sum of planar diagrams. This contradicts a result claimed by De Wit and 't Hooft.