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Systematic Investigations of the Heterotic String Landscape

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Mathematics and Applications of Branes in String and M-theory

Results are reviewed for the first stages of Baylor Universitys ongoing systematic statistics investigations of the parameter space of free fermionic heterotic string models. Presented is the complete set of D = 4, 6 models with either maximal or completely broken spacetime SUSY that are constructed from the untwisted sector and exactly one additional gauge sector containing anywhere from order 2 through 32 twists. All additional models generated to date with additional twisted gauge sectors are also discussed. A vast degeneracy among models appears: from the roughly 2 billion D = 4 models with a single twist sector, only 577 physically distinct models appear. 68 of these have N = 4 SUSY and 509 have completely broken SUSY . To date, no new physically distinct models appear among any of those formed from two or more twisted gauge sectors. Several redundancies among D= 4 models and among D= 6 models are proven to result from redundancies already present among D= 10 models . Methods to reduce redundancies in D= 4, 6 systematic searches are summarized. Statistics regarding the appearance of various combinations of gauge group factors and of GUT groups among the set of 577 physically unique models are presented. Lastly, moving briefly to models with matter sectors, a model with an even number D of large space-time dimensions is shown to always have maximal SUSY , if it is formed from the untwisted sector and a sector with a massless left-mover and an odd ordered right-mover.

This talk is part of the Isaac Newton Institute Seminar Series series.

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