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TMF, 2008, Volume 156, Number 3, Pages 307–327 (Mi tmf6250)  

This article is cited in 3 scientific papers (total in 3 papers)

Moduli spaces of solutions of a noncommutative sigma model

A. V. Domrin

M. V. Lomonosov Moscow State University

Abstract: Using a noncommutative version of the uniton theory, we study the space of those solutions of the noncommutative $U(1)$ sigma model that are representable as finite-dimensional perturbations of the identity operator. The basic integer-valued characteristics of such solutions are their normalized energy $e$, canonical rank $r$, and minimum uniton number $u$, which always satisfy $r\le e$ and $u\le e$. Starting with the so-called BPS solutions ($u=1$), we completely describe the sets of all solutions with $r=1,2,e-1,e$ (which forces $u\le2$) and all solutions of small energy ($e\le5$). The obtained results reveal a simple but nontrivial structure of the moduli spaces and lead to a series of conjectures.

Keywords: noncommutative sigma model, uniton theory

DOI: https://doi.org/10.4213/tmf6250

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English version:
Theoretical and Mathematical Physics, 2008, 156:3, 1231–1246

Bibliographic databases:

Received: 31.07.2007

Citation: A. V. Domrin, “Moduli spaces of solutions of a noncommutative sigma model”, TMF, 156:3 (2008), 307–327; Theoret. and Math. Phys., 156:3 (2008), 1231–1246

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Domrina, “Extended solutions in a noncommutative sigma model”, Proc. Steklov Inst. Math., 279 (2012), 64–72  mathnet  crossref  mathscinet  isi
    2. A. V. Domrina, “Integer-valued characteristics of solutions of the noncommutative sigma model”, Theoret. and Math. Phys., 178:3 (2014), 265–277  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. V. Domrina, A. V. Domrin, “On the Dimension of Solution Spaces of a Noncommutative Sigma Model in the Case of Uniton Number 2”, Proc. Steklov Inst. Math., 298 (2017), 104–117  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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