In this paper, we consider the vacuum energy of a scalar field in the spacetime of two non-parallel cosmic strings. To this end, we obtain metrics for orthogonal straight cosmic strings and for slightly nonparallel strings. In the first case, we derive the separation-dependent part of the vacuum energy in the leading order of string tension. The dependence of the vacuum energy on separation differs from that known for parallel strings. For two strings inclined at a small angle to each other, the approximation used simply reproduces the result for parallel strings, since the angle dependence enters the next to leading order. The results are compared with the Casimir interaction between two inclined cylinders.

中文翻译：

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交叉宇宙弦的真空相互作用

在本文中，我们考虑两个不平行宇宙弦时空标量场的真空能量。为此，我们获得了正交直宇宙弦和稍微不平行的宇宙弦的度量。在第一种情况下，我们以弦张力的前导顺序导出真空能量的分离相关部分。真空能量对分离的依赖性不同于已知的平行串。对于彼此以小角度倾斜的两个弦，所使用的近似值简单地再现了平行弦的结果，因为角度依赖性进入前导阶次。结果与两个倾斜圆柱体之间的 Casimir 相互作用进行了比较。