WEBS OF (P,Q) 5-BRANES, 5 DIMENSIONAL FIELD-THEORIES AND GRID DIAGRAMS

We continue to study 5d N = 1 supersymmetric field theories and their compactifications on a circle through brane configurations. We develop a model, which we call (p, q) Webs, which enables simple geometrical computations to reproduce the known results, and facilitates further s tudy. The physical concepts of field theory are transparent in this pi cture, offering an interpretation for global symmetries, local symmetr ies, the effective (running) coupling, the Coulomb and Higgs branches, the monopole tensions, and the mass of BPS particles. A rule for the dimension of the Coulomb branch is found by introducing Grid Diagrams. Some known classifications of field theories are reproduced. In addit ion to the study of the vacuum manifold we develop methods to determin e the BPS spectrum. Some states, such as quarks, correspond to instant ons inside the 5-brane which we call strips. In general, these may not be identified with (p; q) strings. We describe how a strip can bend o ut of a 5-brane, becoming a string. A general BPS state corresponds to a Web of strings and strips. For special values of the string couplin g a few strips can combine and leave the 5-brane as a string.