1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --

Abstract

We systematically classify 1/2, 1/4 and 1/8 BPS equations in SUSY gauge theories in d=6, 5, 4, 3 and 2 with eight supercharges, with gauge groups and matter contents being arbitrary. Instantons (strings) and vortices (3-branes) are only allowed 1/2 BPS solitons in d=6 with N=1 SUSY. We find two 1/4 BPS equations and the unique 1/8 BPS equation in d=6 by considering configurations made of these field theory branes. All known BPS equations are rederived while several new 1/4 and 1/8 BPS equations are found in dimension less than six by dimensional reductions.

arXiv comment41 pages, no figures, v2: 49 pages, no figures, typos corrected, references added, the final version in NPB

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• Intersecting Solitons, Amoeba and Tropical Geometry
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• Semilocal Fractional Instantons
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• Domain Wall and Three Dimensional Duality
• Noncommutative Q-Lumps