Instantons in the Higgs Phase.pdfVIP

a r X i v : h e p - t h / 0 4 1 2 0 4 8 v 3 2 5 A p r 2 0 0 5 TIT/HEP–530 hep-th/0412048 December, 2004 Instantons in the Higgs Phase Minoru Eto?, Youichi Isozumi?, Muneto Nitta?, Keisuke Ohashi§ and Norisuke Sakai? Department of Physics, Tokyo Institute of Technology Tokyo 152-8551, JAPAN Abstract When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(NC) gauge theory with NF(≥ NC) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an NC × NF ma- trix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed. ?e-mail address: meto@th.phys.titech.ac.jp ?e-mail address: isozumi@th.phys.titech.ac.jp ?e-mail address: nitta@th.phys.titech.ac.jp §e-mail address: keisuke@th.phys.titech.ac.jp ?e-mail address: nsakai@th.phys.titech.ac.jp 1 Introduction Instantons have attracted much attention and have been applied to a wide variety of subjects in physics and mathematics since their discovery [1]. The method to construct multiple instanton solutions was established by Atiyah, Hitchin, Drinfeld and Manin (ADHM) [2] and it was shown that the moduli space of instantons is a hyper-Ka?hler manifold. In supersymmetric (SUSY) gauge theories, instantons play crucial roles as a tool to study non-perturbative