标题： 非相对论展开的开弦和D膜 显示英文标题

标题： Non-relativistic expansion of open strings and D-branes

摘要： 我们将相对论开放玻色弦在$1/c^2$的幂级数中展开，其中$c$是光速。 我们在此展开到次领头阶，在$1/c^2$中并将我们的结果与通过取极限得到的非相对论开放弦的已知描述相关联。 正如封闭弦的情况一样，如果开放弦在目标空间中绕一个圆环卷绕，则非相对论展开是定义良好的。 这一方向必须满足狄利克雷边界条件。 证明了在非相对论 regime 中，开放弦的端点表现为巴格曼粒子。 这些开放弦终止于 nrD$p$-膜上，具有$p\le 24$。 当这些 nrD$p$-膜不发生涨落时，它们对应于目标空间中的$(p+1)$维牛顿-卡坦子流形。 当我们包括涨落和世界体积规范场时，其动力学由一个非相对论版本的DBI作用量描述，我们从对称性考虑推导出其形式。 世界体积规范场和标量场的nrD$24$-膜构成了非相对论电动力学（GED）的场内容，nrD$24$-膜上的有效理论正是GED的一个非线性版本。 我们通过要求它们具有与非相对论开弦和闭弦作用量相同的靶空间规范对称性，将这些结果推广到任何nrD$p$-膜的作用量。 最后，我们证明nrD$p$-膜作用量是横向T对偶协变的。 我们的结果与Gomis、Yan和Yu在arXiv:2007.01886中的发现一致。 显示英文摘要

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.