This article is cited in 1 paper

Description of solutions with the uniton number $3$ in the case of one eigenvalue: Counterexample to the dimension conjecture

A. V. Domrina

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Moscow, Russia

Abstract: We explicitly describe solutions of the noncommutative unitary $U(1)$ sigma model that represent finite-dimensional perturbations of the identity operator and have only one eigenvalue and the minimum uniton number $3$. We also show that the solution set $M(e,r,u)$ of energy $e$ and canonical rank $r$ with the minimum uniton number $u=3$ has a complex dimension greater than $r$ for $e=4n-1$ and $r=n+1$, where $n\ge3$. This disproves the dimension conjecture that holds in the case $u\in\{1,2\}$.

Keywords: noncommutative sigma model, uniton theory.

Received: 17.01.2019
Revised: 17.01.2019

DOI: 10.4213/tmf9700

 English version: Theoretical and Mathematical Physics, 2019, 201:1, 1413–1425

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