发表机构
Universidad de Guanajuato（瓜纳华托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究IIB型弦论单参数Calabi-Yau三维流形通量势中精细德西特猜想、跨普朗克审查猜想与物种尺度界限，发现势斜率满足RdSC，TCC给出体积下限。
AI 中文摘要
我们研究了精细的德西特猜想（RdSC）、跨普朗克审查猜想（TCC）以及物种尺度$\Lambda_s$，这些研究是在IIB型弦理论紧化于单参数Calabi-Yau三维流形上的多场通量势中进行的。标量势依赖于轴子-膨胀子场和单一复结构模量，并沿Kähler方向呈现无标度结构。限制在$h^{2,1}=1$使得我们可以使用从Picard-Fuchs方程获得的精确周期，而不是其大复结构展开，从而能够探测锥形区域。对于镜像五次流形，$(h^{2,1},h^{1,1})=(1,101)$，我们扫描了200种通量构型，发现96%的情况下存在不稳定极值点，其中$c'=0.18$。一旦考虑到Kähler逃逸，无标度结构将每个临界点处势的对数斜率固定为普适值$\sqrt{6}$，因此第一个RdSC条件在整个过程中得到满足。统计上，复结构是较重的扇区，而轴子-膨胀子主导不稳定方向。对于TCC，我们获得了适用于整个单参数模型类的解析结果：斜率在大复结构处趋近普适值$2$，在锥形区域发散，并且在轴子-膨胀子方向上恰好等于$\sqrt{2}$，其中主导势采用单一的$SL(2)$协变形式，多场演化数值结果也证实了这一点。TCC进一步转化为对紧化体积的下限，$v>v_0\sim e^{N}$，该下限由e折叠数控制。最后，沿我们轨迹的场位移与物种尺度场范围界限相容，并且恢复$\Lambda_s$的体积依赖性表明$V\lesssim3\Lambda_s^2$由TCC体积界限隐含，因此这是对这些模型的真正约束。
英文摘要
We study the refined de Sitter conjecture (RdSC), the Trans-Planckian Censorship Conjecture (TCC) and the species scale $Λ_s$ in the multifield flux potential of type IIB string theory compactified on one-parameter Calabi--Yau threefolds. The scalar potential depends on the axio-dilaton and on the single complex-structure modulus, and is no-scale along the Kähler directions. Restricting to $h^{2,1}=1$ allows us to work with the exact periods obtained from the Picard--Fuchs equations rather than with their large-complex-structure expansion, and therefore to probe the conifold region. For the mirror quintic, $(h^{2,1},h^{1,1})=(1,101)$, we scan 200 flux configurations and find unstable extrema in $96\%$ of the cases, with $c'=0.18$. Once the Kähler runaway is taken into account, the no-scale structure fixes the logarithmic slope of the potential at every critical point to the universal value $\sqrt6$, so that the first RdSC condition is satisfied throughout. Statistically, the complex structure is the heavier sector and the axio-dilaton dominates the unstable directions. For the TCC we obtain analytic results valid for the whole class of one-parameter models: the slope approaches the universal value $2$ at large complex structure, diverges at the conifold, and equals exactly $\sqrt2$ in the axio-dilaton directions, where the leading potential takes a single $SL(2)$-covariant form, as the multifield evolutions confirm numerically. The TCC further translates into a lower bound on the compactification volume, $v>v_0\sim e^{N}$, controlled by the number of e-folds. Finally, the field displacements along our trajectories are compatible with the species-scale field-range bound, and restoring the volume dependence of $Λ_s$ shows that $V\lesssim3Λ_s^2$ is implied by the TCC volume bound, which is thus the genuine constraint on these models.
