Webs of (p,q) 5-branes, Five 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 study. The physical concepts of field theory are transparent in this picture, offering an interpretation for global symmetries, local symmetries, 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 addition to the study of the vacuum manifold we develop methods to determine the BPS spectrum. Some states, such as quarks, correspond to instantons 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 out 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 coupling a few strips can combine and leave the 5-brane as a string.Comment: 72 pages, latex, 25 figures, references and small corrections adde

Analytic Evidence for Continuous Self Similarity of the Critical Merger Solution

The double cone, a cone over a product of a pair of spheres, is known to play a role in the black-hole black-string phase diagram, and like all cones it is continuously self similar (CSS). Its zero modes spectrum (in a certain sector) is determined in detail, and it implies that the double cone is a co-dimension 1 attractor in the space of those perturbations which are smooth at the tip. This is interpreted as strong evidence for the double cone being the critical merger solution. For the non-symmetry-breaking perturbations we proceed to perform a fully non-linear analysis of the dynamical system. The scaling symmetry is used to reduce the dynamical system from a 3d phase space to 2d, and obtain the qualitative form of the phase space, including a non-perturbative confirmation of the existence of the "smoothed cone".Comment: 25 pages, 4 figure

Thermal Monopoles

Evidence is given that some particles with large charges in gauge theories, including 4d N=4 SU(3) and 5d theories with N=1 supersymmetry, have macroscopic entropy. The ground state entropy is found to be extensive in the charges. The mass gap for excitation is estimated and is of the same order as the binding energy. The question of the decay of excited states through Hawking radiation is raised. The analysis is based on the model of (p,q) string webs and on various other results. The evidence points to an explanation in terms of a string model.Comment: 12 pages. JHEP modified version, see note added to introductio