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

This article is cited in 4 scientific papers (total in 4 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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  • https://doi.org/10.4213/tmf6250
  • http://mi.mathnet.ru/eng/tmf/v156/i3/p307

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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  elib
    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
    4. A. V. Domrina, “Description of solutions with the uniton number $3$ in the case of one eigenvalue: Counterexample to the dimension conjecture”, Theoret. and Math. Phys., 201:1 (2019), 1413–1425  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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