标题： 模对称性、阈值修正及$Z_2 \times Z_2 $透镜体的模空间 显示英文标题

标题： Modular Symmetries, Threshold Corrections And Moduli For $Z_2 \times Z_2 $ Orbifolds

摘要： ${\bf Z}_2\times {\bf Z}_2$ 具有特定性质的Coxeterorbifold被构建出来，其中一些扭曲扇区具有固定平面，对于这些固定平面，六维环面不能分解为直接和${\bf T}^2\bigoplus{\bf T}^4 $ 的形式，且固定平面位于${\bf T}^2$中。 推导了弦环阈值修正对规范耦合常数的影响，并展示了对于$T$和$U$模量的对称群是全模群$PSL(2,Z)$的子群。 在存在隐藏部门物质的情况下，构建了对偶不变的gauino凝聚的有效势，并针对模量的值进行了最小化。 还研究了威尔逊线对模对称性的影响。 显示英文摘要

摘要： ${\bf Z}_2\times {\bf Z}_2$ Coxeter orbifolds are constructed with the property that some twisted sectors have fixed planes for which the six-torus can not be decomposed into a direct sum ${\bf T}^2\bigoplus{\bf T}^4 $ with the fixed plane lying in ${\bf T}^2$. The string loop threshold corrections to the gauge coupling constants are derived, and display symmetry groups for the $T$ and $U$ moduli that are subgroups of the full modular group $PSL(2,Z)$. The effective potential for duality invariant gaugino condensate in the presence of hidden sector matter is constructed and minimized for the values of the moduli. The effect of Wilson lines on the modular symmetries is also studied.