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In the light of recent experimental results for the direct detection of dark matter, we analyze in the framework of SUGRA the value of the neutralino-nucleon cross section. We study how this value is modified when the usual assumptions of universal soft terms and GUT scale are relaxed. In particular we consider scenarios with non-universal scalar and gaugino masses and scenarios with intermediate unification scale. We also study superstring constructions with D-branes, where a combination of the above two scenarios arises naturally. In the analysis we take into account the most recent experimental constraints, such as the lower bound on the Higgs mass, the $b\to s\gammag-2$.

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