Moduli spaces of solutions of a~noncommutative sigma model
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 307-327
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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.
@article{TMF_2008_156_3_a0,
author = {A. V. Domrin},
title = {Moduli spaces of solutions of a~noncommutative sigma model},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {307--327},
publisher = {mathdoc},
volume = {156},
number = {3},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a0/}
}
A. V. Domrin. Moduli spaces of solutions of a~noncommutative sigma model. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 307-327. http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a0/