用S类理论对沼泽界进行压力测试
Stress-Testing Swampland Bounds with Class S Theories
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中文总结 AI 辅助
本文以S类理论为研究对象，通过AdS₅时空的CFT对偶，测试了SharpDC与RDC，证明了SharpDC在特定大N超对称规范理论中成立，发现其在S类理论的极限下被违反，并得到RDC的精确上界。
中文摘要 AI 辅助
我们利用共形场论（CFT）对偶，在AdS₅引力时空中测试CFT的锐化距离猜想（SharpDC）以及改进距离猜想（RDC）。前者为共形流形上无穷远处变轻的态塔的指数质量衰减率提供下界，后者则限定在态塔指数行为出现前可穿越的体场范围。我们证明，对于任意具有有限个规范因子M且单圈β函数为零的大N拉格朗日超对称规范理论，SharpDC成立。我们还研究了它是否在大中心荷极限下普遍成立，发现并非如此：我们给出了S类理论中的具体例子，当N固定且M→∞时，该猜想被违反，此时体内部几何的尺度远大于AdS曲率尺度。我们还在大N极限下无孔的S类理论模空间中测试了RDC，表明它构成了对亏格为g的黎曼曲面模空间的Weil-Petersson直径的精确上界。该界与迄今为止所有数学文献一致，但至今仍未被证明。
英文摘要
We test the Sharpened Distance Conjecture (SharpDC) for CFTs, as well as the Refined Distance Conjecture (RDC), in AdS$_5$ gravitational spacetimes, using the CFT dual. The former provides a lower bound on the exponential mass decay rate of the tower of states becoming light at infinite distance in the conformal manifold, while the latter bounds the bulk field range that can be traversed before the exponential behaviour of the tower kicks in. We prove the SharpDC for any large $N$ Lagrangian supersymmetric gauge theory with a finite number $M$ of gauge factors and vanishing one-loop $β$-function. We also investigate whether it universally holds in the limits of large central charge, finding that it does not: We exhibit concrete examples in Class S theories where the conjecture is violated in the $M\rightarrow\infty$ limit with $N$ fixed, where the size of the bulk internal geometry is much larger than the AdS curvature scale. We also test the RDC in the moduli space of Class S theories without punctures in the large $N$ limit, showing that it amounts to a precise upper bound on the Weil-Petersson diameter of the moduli space of Riemann surfaces of genus $g$. This bound is consistent with all the mathematical literature up to date, but so far remains unproven.
