发表机构
Indian Institute of Science（印度科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文研究四维轴子虫洞的边界条件，通过对偶标量与三形式通量公式分析得出跨喉鞍点无贡献，且其结论与虚距离界及KSW准则一致。
AI 中文摘要
我们利用对偶标量和三形式通量公式，研究洛伦兹极小超空间路径积分中的四维轴子虫洞。我们针对一般度规边界条件和实时缩积分轮廓分析该对偶性，并证明其在任意背景（包括复背景）上均成立。在度规的狄利克雷条件下，固定通量的路径积分可精确计算。在欧几里得区域，鞍点几何按Giddings-Strominger（GS）虫洞的同侧和跨喉段划分，取决于两个边界是否位于喉的同侧或对侧。对时缩覆盖平面的皮卡-勒夫谢茨分析表明，跨喉鞍点的相交数为零，因此无贡献。在渐近平坦极限下，它对应满足虚距离界（IDB）的虚虫洞。对偶的标量侧独立得出相同结论，并由精确振幅确认。将狄利克雷条件替换为单参数诺伊曼条件，导致虚虫洞的跨喉鞍点仍与轮廓的物理提升无关。表征诺伊曼条件的纯虚参数在半虫洞和全虫洞几何之间连续插值。固定电荷扇区求和的收敛性对边界轴子的虚部以及表征诺伊曼边界条件的参数施加了相应的插值界。基于KSW准则的独立分析精确再现了相同的界，强调其与IDB的兼容性。
英文摘要
We study four-dimensional axion wormholes in the Lorentzian mini-superspace path integral using dual scalar and three-form flux formulations. We analyze this duality for generic metric boundary conditions and real lapse integration contour, and show that it holds on any background, including complex ones. With the Dirichlet condition on the metric, the fixed-flux path integral is evaluated exactly. In the Euclidean regime, saddle geometries organize into same-side and cross-throat segments of the Giddings-Strominger (GS) wormhole, depending on whether the two boundaries lie on the same or opposite sides of the throat. A Picard-Lefschetz analysis in the covering plane of lapse reveals that the cross-throat saddle has vanishing intersection number, and therefore does not contribute. In the asymptotically flat limit, it corresponds to the imaginary wormhole that saturates the imaginary distance bound (IDB). The same conclusion follows independently on the scalar side of the duality, and is confirmed by the exact amplitude. Replacing the Dirichlet condition with a one-parameter Neumann condition, the cross-throat saddle that leads to the imaginary wormholes remains irrelevant for the physical lift of the contour. This purely imaginary parameter characterizing the Neumann condition interpolates continuously between the half- and complete-wormhole geometries. Convergence of the sum over fixed-charge sectors imposes a corresponding interpolating bound not only on the imaginary part of the boundary axion but also on the parameter characterizing the Neumann boundary condition. An independent analysis based on the KSW criterion reproduces exactly the same bound, emphasizing its compatibility with the IDB.
Commentsv1: 1+42 pages, 15 figures, 2 tables, 6 appendices
