Nonsingular solutions of Hitchin's equations for noncompact gauge groups
Nonsingular solutions of Hitchin's equations for noncompact gauge groups
复制标题
非紧规范组希钦方程的非奇异解
DOI：
10.1088/0951-7715/20/8/005
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发表时间：
2006
期刊：
影响因子：
1.7
通讯作者：
M. Jardim
中科院分区：
文献类型：
--
作者：
R. A. Mosna;M. Jardim
我们考虑了一种求解二维Hitchin方程的一般方法，它是由四维自对偶杨-Mills方程降维而产生的，具有显著的可积性。我们主要讨论规范群G由实数形式给出的情形。对于G=SO(2，1)，所得到的场方程化成Liouville方程、椭圆Sinh-Gordon方程或椭圆Sine-Gordon方程。与G=SU(2)给出的紧性情形相反，与非紧性群SO(2，1)相关的场方程组具有非奇异作用密度的光滑实解，并且在某种意义上是局部化的。最后，我们讨论了在S2和T2中定义的一些特殊解，这些解来自于这个ansatz。
We consider a general ansatz for solving the 2-dimensional Hitchin's equations, which arise as dimensional reduction of the 4-dimensional self-dual Yang–Mills equations, with remarkable integrability properties. We focus on the case when the gauge group G is given by a real form of . For G = SO(2,1), the resulting field equations are shown to reduce to either the Liouville, elliptic sinh-Gordon or elliptic sine-Gordon equations. As opposed to the compact case, given by G = SU(2), the field equations associated with the noncompact group SO(2,1) are shown to have smooth real solutions with nonsingular action densities, which are furthermore localized in some sense. We conclude by discussing some particular solutions, defined on , S2 and T2, that come out of this ansatz.