Neumann-Dirichlet开弦的单圈质量与边界变化顶点算子
One-loop masses of Neumann-Dirichlet open strings and boundary-changing vertex operators
摘要：
当超对称性自发破缺时，我们导出了开弦的Neumann-Dirichlet扇区中无质量标量在一个环上获得的质量。它是通过计算两点函数的“边界改变顶点算子”插入的边界上的环和莫比乌斯带。这就需要评估“受激边界变化场”的耗散子，它类似于封闭弦的受激扭曲场。我们工作在IIB型orientifold理论紧化的$T^2\times T^4/\mathbb{Z}_2$，其中$\mathcal{N}=2$超对称性被打破$\mathcal{N}=0$的Scherk-Schwarz机制实现沿$T^2$。尽管平方质量的完整表达式是复杂的，但当背景的最低标度是超对称破缺标度$M_{3/2}$时，它简化为非常简单的形式。我们应用我们的结果来分析在这个政权的稳定性在量子水平上的模场产生的纽曼-狄利克雷部门。这就完成了参考文献[32]的研究，其中导出了开弦或闭弦扇区中所有其他类型模的量子质量。最终，我们确定所有的膜配置，产生背景没有快子在一个循环，并产生一个有效的潜在指数抑制，或严格的积极与失控行为的$M_{3/2}$。
英文摘要：
We derive the masses acquired at one loop by massless scalars in the Neumann-Dirichlet sector of open strings, when supersymmetry is spontaneously broken. It is done by computing two-point functions of "boundary-changing vertex operators" inserted on the boundaries of the annulus and Möbius strip. This requires the evaluation of correlators of "excited boundary-changing fields," which are analogous to excited twist fields for closed strings. We work in the type IIB orientifold theory compactified on $T^2\times T^4/\mathbb{Z}_2$, where $\mathcal{N}=2$ supersymmetry is broken to $\mathcal{N}=0$ by the Scherk-Schwarz mechanism implemented along $T^2$. Even though the full expression of the squared masses is complicated, it reduces to a very simple form when the lowest scale of the background is the supersymmetry breaking scale $M_{3/2}$. We apply our results to analyze in this regime the stability at the quantum level of the moduli fields arising in the Neumann-Dirichlet sector. This completes the study of Ref. [32], where the quantum masses of all other types of moduli arising in the open- or closed-string sectors are derived. Ultimately, we identify all brane configurations that produce backgrounds without tachyons at one loop and yield an effective potential exponentially suppressed, or strictly positive with runaway behavior of $M_{3/2}$.
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