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

Masashi Naganuma, Muneto Nitta, Norisuke Sakai

Abstract

BPS lumps in ${\cal N}=2$ 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 ${\cal N}=2$ SUSY nonlinear sigma models with (without) a potential term. These BPS states include non-parallel multi-(Q-)lumps.

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

Abstract

BPS lumps in 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 SUSY nonlinear sigma models with (without) a potential term. These BPS states include non-parallel multi-(Q-)lumps.

Paper Structure

This paper contains 15 sections, 54 equations.

Table of Contents

  1. Introduction
  2. 1/2 BPS lumps in D=4 hyper-Kähler nonlinear sigma models
  3. Hyper-Kähler manifold
  4. D=4 HK nonlinear sigma models
  5. Lumps and BPS condition
  6. Lump solution in multi-center metric
  7. Multi-center models
  8. General lump solution as holomorphic map
  9. Lump in 2-center models
  10. Lumps in 3-center models
  11. BPS equation for coexisting lumps
  12. New BPS bound and BPS equation in HK nonlinear sigma models
  13. BPS condition for coexistence of lumps
  14. Lump intersections and multi-center metric
  15. Summary and discussions