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arXiv 2008.08895hep-th
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非相对论性自旋弦

Nonrelativistic spinning strings

Dibakar Roychowdhury

摘要:

在$ AdS_5 \times S^5 $中构造了对应于弦的$ SU(1,2|3) $自旋矩阵理论(SMT)极限的非相对论自旋弦解.考虑到$ AdS_5 $和$ S^5 $中的各种非相对论自旋弦构型,我们得到了SMT强耦合区中相应的色散关系,其中在$ AdS_5 $中弦的慢自旋极限下,BPS边界附近的强耦合($ \sim \sqrt{\mathfrak{g}} $)修正已被估计.我们通过构造三个自旋折叠弦构型来推广我们的结果,其中两个自旋沿着$ AdS_5 $,一个沿着$ S^5 $。我们的分析表明,对谱的修正依赖于$ AdS_5 $中NR弦的长度。本文的其余部分基本上揭示了$ AdS_5 \times S^5 $中弦的$ SU(1,2|3) $自旋矩阵理论(SMT)极限与一维非相对论性Neumann-Rosochatius类可积模型之间的潜在联系。以两个具体的例子NR自旋字符串在$ R \times S^3 $以及在某些子部门的$ AdS_5 $,我们表明,类似的减少确实是可能的,其中一个可以估计的频谱的理论使用一维模型。

英文摘要:

We construct nonrelativistic spinning string solutions corresponding to $ SU(1,2|3) $ Spin-Matrix theory (SMT) limit of strings in $ AdS_5 \times S^5 $. Considering various nonrelativistic spinning string configurations both in $ AdS_5 $ as well as $ S^5 $ we obtain corresponding dispersion relations in the strong coupling regime of SMT where the strong coupling ($ \sim \sqrt{\mathfrak{g}} $) corrections near the BPS bound have been estimated in the slow spinning limit of strings in $ AdS_5 $. We generalize our results explicitly by constructing three spin folded string configurations that has two of its spins along $ AdS_5 $ and one along $ S^5 $. Our analysis reveals that the correction to the spectrum depends non trivially on the length of the NR string in $ AdS_5 $. The rest of the paper essentially unfolds the underlying connection between $ SU(1,2|3) $ Spin-Matrix theory (SMT) limit of strings in $ AdS_5 \times S^5 $ and the nonrelativistic Neumann-Rosochatius like integrable models in 1D. Taking two specific examples of NR spinning strings in $ R \times S^3 $ as well as in certain sub-sector of $ AdS_5 $ we show that similar reduction is indeed possible where one can estimate the spectrum of the theory using 1D model.

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