论文标题
非相关的弦乐单粒
Non-relativistic string monodromies
论文作者
论文摘要
在相对论的集成字符串理论的上下文中，光谱曲线方法被证明是强大的技术，因为它们允许从LAX对的最小知识和经典的字符串解决方案中得出半经典光谱。在本文中，我们启动了ADS $ _5 \ TIMES s^5 $的非相关字符串的光谱曲线的研究。首先，我们证明，对于Lax连接的弦溶液与$σ$无关，单构矩阵的特征值没有任何频谱参数依赖性。我们指出，这种特殊的行为也用于平坦空间中的相对论字符串。其次，对于一些可以计算LAX连接的路径有序指数的简单非相关弦溶液，我们表明单型矩阵可以对角线呈斜矩阵，而quasi-momenta独立于光谱参数，或者是不可用的。对于后一种情况，我们基于最大的Abelian subselgerbras提出了广义准摩部分的概念，该概念保留了对频谱参数的依赖。
Spectral curve methods proved to be powerful techniques in the context of relativistic integrable string theories, since they allow to derive the semiclassical spectrum from the minimal knowledge of a Lax pair and a classical string solution. In this paper we initiate the study of the spectral curve for non-relativistic strings in AdS$_5\times S^5$. First we show that for string solutions whose Lax connection is independent of $σ$, the eigenvalues of the monodromy matrix do not have any spectral parameter dependence. We remark that this particular behaviour also appears for relativistic strings in flat space. Second, for some simple non-relativistic string solutions where the path ordered exponential of the Lax connection can be computed, we show that the monodromy matrix is either diagonalisable with quasi-momenta independent of the spectral parameter, or non-diagonalisable. For the latter case, we propose a notion of generalised quasi-momenta, based on maximal abelian subalgebras, which retain a dependence on the spectral parameter.
