• DOI:10.1088/1126-6708/2002/01/011
• Corpus ID: 14727244

Scalar Multi-Solitons on the Fuzzy Sphere

@article{Vaidya2001ScalarMO,
  title={Scalar Multi-Solitons on the Fuzzy Sphere},
  author={Sachindeo Vaidya},
  journal={Journal of High Energy Physics},
  year={2001},
  volume={2002},
  pages={011-011}
}

• S. Vaidya
• Published 13 September 2001
• Mathematics, Physics
• Journal of High Energy Physics

We study solitons in scalar theories with polynomial interactions on the fuzzy sphere. Such solitons are described by projection operators of rank k, and hence the moduli space for the solitons is the grassmannian Gr(k,2j+1). The gradient term of the action provides a non-trivial potential on Gr(k,2j+1), thus reducing the moduli space. We construct configurations corresponding to well-separated solitons, and show that although the solitons attract each other, the attraction vanishes in the limit of large j. In this limit, it is argued that the moduli space is (1)⊗k/k k. For the k-soliton bound state, the moduli space is simply 1, all other moduli being lifted. We find that the moduli space of multi-solitons is smooth and that there are no singularities as several solitons coalesce. When the fuzzy S2 is flattened to a noncommutative plane, we find agreement with the known results, modulo some operator-ordering ambiguities. This suggests that the fuzzy sphere is a natural way to regulate the noncommutative plane both in the ultraviolet and infrared.