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arXiv 2211.04479hep-th
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非相对论弦单值性

Non-relativistic string monodromies

Andrea Fontanella, Juan Miguel Nieto García, Olof Ohlsson Sax

摘要:

在相对论可积弦论中,谱曲线方法被证明是一种强大的技术,因为它们允许从拉克斯对和经典弦解的最小知识中推导出半经典谱。本文首次研究了AdS $_5\times S^5$中非相对论弦的谱曲线。首先,我们表明,对于弦的解决方案,其Lax连接是独立的$σ$,monodromy矩阵的特征值没有任何谱参数的依赖。我们注意到,这种特殊的行为也出现在相对论弦在平坦空间。其次,对于一些简单的非相对论性的弦解,其中的路径有序指数的Lax连接可以计算,我们证明了monodromy矩阵是对角化的与谱参数无关的准动量,或non-diagonalisable。对于后者的情况下,我们提出了一个广义准动量的概念,基于极大阿贝尔子代数,保留依赖的谱参数。

英文摘要:

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.

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