BPS Spectrum of 5 Dimensional Field Theories, (p,q) Webs and Curve Counting

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  • 13 January 1998
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 highest spin, j, is determined by the number of deformations of the string web, n_{df}, to be 2j=n_{df} (j=0 is a hyper and j=1/2 is a vector). 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. We infer that the highest spin of the membrane (or largest multiplet type) is given by 2j=h+g-1, where h is the number of holes (boundaries) and g is the genus. Mathematically, we obtain a diagrammatic method to find the spectrum of curves on a toric complex surface, and the number of their moduli.

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