BPS Lumps and Their Intersections in $\mathcal{N}=2$ SUSY Nonlinear Sigma Models

Abstract

BPS lumps in $\mathcal{N}=2$ SUSY nonlinear sigma models on hyper-\kahler manifolds in four dimensions are studied. We present new lump solutions with various kinds of topological charges. New BPS equations and a new BPS bound, expressed by the three complex structures on hyper-\kahler manifolds, are found. We show that any states satisfying these BPS equations preserve 1/8 (1/4) SUSY of $\mathcal{N}=2$ SUSY nonlinear sigma models with (without) a potential term. These BPS states include non-parallel multi-(Q-)lumps.

19pages, submitted to G\@C, special issue devoted to Quantum Gravity, Unified Models and Strings to mark 100th anniversary of Tomsk state Pedagogical University, Editor-Prof.S.D. Odintsov, Signs of SUSY conditions are corrected in a few points

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