## Abstract

We study the BPS spectrum of supersymmetric 5 dimensional field theories and their representations as string webs. It is found that a state of given charges exists when it has a representation as an irreducible string web. Its spin is determined by the string web. The number of fermionic zero modes is 8g + 46, where g is the number of internal faces and b is the number of boundaries. In the lift to M theory of 4d field theories such states are described by membranes ending on the 5-brane, breaking SUSY from 8 to 4, and g becomes the genus of the membrane. Mathematically, we obtain a diagrammatic method to find the spectrum of curves on a toric complex surface, and the number of their moduli.

Original language | American English |
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Pages (from-to) | XVI-14 |

Journal | Journal of High Energy Physics |

Volume | 2 |

Issue number | 8 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

## Keywords

- Brane Dynamics in Gauge Theories
- Field Theories in Higher Dimensions
- M-Theory
- Solitons Monopoles and Instantons