arXiv 2407.059852024-07-08hep-th

开弦与D-膜的非相对论展开

Non-relativistic expansion of open strings and D-branes

Jelle Hartong, Emil Have

备注：: 46 pages, 1 figure

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AI总结：

本文对开玻色弦进行 $1/c^2$ 非相对论展开至次领头阶，揭示开弦端点表现为巴格曼粒子并终止于 nrD$p$-膜，进而由对称性推导出非相对论 DBI 作用量，并证明其横向 T-对偶协变性。

摘要：

我们将相对论性开玻色弦按 $1/c^2$ 的幂次展开，其中 $c$ 为光速。我们对该展开进行到 $1/c^2$ 的次领头阶，并将结果与通过取极限得到的已知非相对论开弦描述联系起来。与闭弦情形一样，如果开弦在目标空间中缠绕一个圆，则非相对论展开是良定义的。该方向必须满足狄利克雷边界条件。研究表明，在非相对论区域中，开弦的端点表现为巴格曼粒子。这些开弦终止于 nrD$p$-膜，且 $p\le 24$。当这些 nrD$p$-膜不发生涨落时，它们对应于目标空间的 $(p+1)$ 维牛顿-嘉当子流形。当我们纳入涨落和世界体规范场时，其动力学由一个非相对论版本的 DBI 作用量描述，其形式由对称性考虑推导得出。nrD$24$-膜的世界体规范场和标量场构成伽利略电动力学（GED）的场内容，且 nrD$24$-膜上的有效理论恰为 GED 的非线性版本。我们将这些结果推广到任意 nrD$p$-膜的作用量，要求它们具有与非相对论开弦和闭弦作用量相同的目标空间规范对称性。最后，我们证明 nrD$p$-膜作用量在横向 T-对偶下是协变的。我们的结果与 Gomis、Yan 和 Yu 在 arXiv:2007.01886 中的发现一致。

英文摘要：

We expand the relativistic open bosonic string in powers of $1/c^2$ where $c$ is the speed of light. We perform this expansion to next-to-leading order in $1/c^2$ and relate our results to known descriptions of non-relativistic open strings obtained by taking limits. Just as for closed strings the non-relativistic expansion is well-defined if the open string winds a circle in the target space. This direction must satisfy Dirichlet boundary conditions. It is shown that the endpoints of the open string behave as Bargmann particles in the non-relativistic regime. These open strings end on nrD$p$-branes with $p\le 24$. When these nrD$p$-branes do not fluctuate they correspond to $(p+1)$-dimensional Newton--Cartan submanifolds of the target space. When we include fluctuations and worldvolume gauge fields their dynamics is described by a non-relativistic version of the DBI action whose form we derive from symmetry considerations. The worldvolume gauge field and scalar field of a nrD$24$-brane make up the field content of Galilean electrodynamics (GED), and the effective theory on the nrD$24$-brane is precisely a non-linear version of GED. We generalise these results to actions for any nrD$p$-brane by demanding that they have the same target space gauge symmetries that the non-relativistic open and closed string actions have. Finally, we show that the nrD$p$-brane action is transverse T-duality covariant. Our results agree with the findings of Gomis, Yan and Yu in arXiv:2007.01886.

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