Webs of (p,q) 5-branes, five dimensional field theories and grid diagrams

Ofer Aharony*, Amihay Hanany, Barak Kol

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

220 Scopus citations


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.

Original languageAmerican English
Pages (from-to)XII-48
JournalJournal of High Energy Physics
Issue number1
StatePublished - 1998
Externally publishedYes


  • Field Theories in Higher Dimensions
  • M- and F-theories and Other Generalizations
  • Nonperturbative Approaches
  • Solitons Monopoles and Instantons


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