Seiberg–Witten monopole equations on noncommutative R4
Seiberg–Witten monopole equations on noncommutative R4
复制标题
非交换 R4 上的 Seiberg-Witten 单极方程
DOI：
10.1063/1.1604454
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发表时间：
2003
影响因子：
1.3
通讯作者：
Martin Wolf
中科院分区：
文献类型：
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作者：
A. D. Popov;A. Sergeev;Martin Wolf
众所周知，在欧几里得四维空间R4上，由于消去定理，Abelian Seiberg-Witten(SW)单极子方程不存在非平凡的有限作用解。我们证明了这对非对易形式的方程不再成立，即在R4的非对易变形Rθ4上，具有非零拓扑电荷的SW方程存在光滑解。我们引入了非对易SW方程的作用泛函，并构造了显式正则解。我们所有的解都有有限的能量。对于第二类超弦理论中DP-DP膜系统中的D(p−4)-膜和D(p−4)膜系，我们还提出了一种可能的解释为表示D(p-Dp 4)-膜和D(p-Dp-4)膜系的余维四个类涡旋孤子.
It is well known that, due to vanishing theorems, there are no nontrivial finite action solutions to the Abelian Seiberg–Witten (SW) monopole equations on Euclidean four-dimensional space R4. We show that this is no longer true for the noncommutative version of these equations, i.e., on a noncommutative deformation Rθ4 of R4 there exist smooth solutions to the SW equations having nonzero topological charge. We introduce action functionals for the noncommutative SW equations and construct explicit regular solutions. All our solutions have finite energy. We also suggest a possible interpretation of the obtained solutions as codimension four vortex-like solitons representing D(p−4)- and D(p−4)¯-branes in a Dp-Dp¯ brane system in type II superstring theory.