消失与定向折叠锥形的Riemann-Hilbert问题
Crosscap resurgence and Riemann--Hilbert problems for orientifolded conifolds
AI总结：
本文研究了大N SO/Sp 折叠锥形自由能的crosscap部分，通过q-Pochhammer塔和Faddeev量子对数积分的函数方程，推导了Borel变换、极点结构和Stokes跃迁等性质，并结合解析总结定理得到大N定向折叠自由能的消失陈述。
摘要：
我们研究了大N SO/Sp 折叠锥形自由能的crosscap部分。未投影的crosscap块是一个单一的q-Pochhammer塔。其秩一移位方程匹配Faddeev量子对数积分的函数方程，在变量变换后。利用已知的Borel-消失定理，我们计算了原始块及其奇投影的Borel变换、极点结构、扇区和、Stokes跃迁以及极限扇区。将奇投影crosscap计算与解析总结定理结合，得到大N定向折叠自由能的相应消失陈述。我们还提出了一个公理化的经典自对偶Riemann-Hilbert问题，其局部墙穿越因子从crosscap Stokes跃迁中提取。该构造使用了双倍电荷晶格和选定的O-平面发生函数。在该公理化设定中，归一化的标量crosscap扇区函数给出τ-函数，其基本移位比率解决坐标问题。
英文摘要：
We study the crosscap contribution to the large-$N$ SO/Sp free energy of the orientifolded conifold by comparing its formal expansion with Faddeev's quantum dilogarithm. This determines its Borel transform, sectorial sums, Stokes jumps, and accumulation limits; in the convergent chamber, these limits combine with resolved-conifold summation to recover the full orientifold free energy. We also construct a convergent ray-finite uncoupled rank-five rational BPS structure supported on the finite crosscap rays, and show that its Stokes tails violate both unrestricted half-plane normalization and two-sided polynomial growth at the non-active accumulation rays. Restricting normalization to closed subsectors and dropping the growth condition at those rays yields a unique solution expressed in terms of normalized double-sine functions. Finally, finite differences of the scalar Stokes transition recover the two BPS character multipliers and determine the supported active rational invariants.
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