从10维有效场论视角推导LVS的尝试
An attempt to derive the LVS from a 10d EFT perspective
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中文总结 AI 辅助
本文从10维有效场论视角尝试推导LVS势，发现体积抑制因子与4维超引力预期不符，虽探讨了可能原因但未能解决，指出Kähler势修正或需足够强且来源不明。
中文摘要 AI 辅助
非微扰标量势是通量紧致化中稳定模场的核心要素。在此背景下，一个关键目标是直接进行LVS AdS势的10维推导，即大体积场景在uplift之前的标量势。依赖于4维超引力机制和大体积展开的已知结果由三项参数形式组成：$\exp(-2a\tau_s)/{\mathcal V}$、$W_0\exp(-a\tau_s)/{\mathcal V}^2$和$W_0^2/{\mathcal V}^3$。在纯10维有效场论语言中，第一项是瞬子-反瞬子效应，而第二项来自与3形式通量耦合的单瞬子。当试图直接从10维有效场论推导体积${\mathcal V}$的抑制时，会遇到一个难题：对于第二项，预期存在通量稀释因子$1/\sqrt{\mathcal V}$，而对于第一项和第二项，通过Weyl标度变换到4维爱因斯坦框架会得到因子$1/{\mathcal V}^2$。因此，这两项的总体积抑制比前述4维有效场论预期更强。我们详细讨论了其背后的逻辑，也涉及规范凝聚情形，但未能找到对这种不匹配的满意解释。虽然Kähler势的对数修正可能是原因，但这些修正必须足够强，才能在${\mathcal O}(1)$级别影响LVS方案的结果。更糟糕的是，所需修正的起源仍不清楚。
英文摘要
Non-perturbative scalar potentials are a central ingredient for stabilising moduli in flux compactifications. A key target in this context is the direct 10d derivation of the LVS AdS potential, i.e., the scalar potential of the Large Volume Scenario before the uplift. The familiar result, relying on 4d supergravity machinery and large volume expansion, consists of three terms of parametric form $\exp(-2aτ_s)/{\mathcal V}$, $W_0\exp(-aτ_s)/{\mathcal V}^2$, and $W_0^2/{\mathcal V}^3$. In plain 10d EFT language, the first term is an instanton-anti-instanton effect while the second term comes from a single instanton coupled to 3-form flux. When attempting to derive the suppression by the volume ${\mathcal V}$ directly from the 10d EFT, one encounters a puzzle: One expects a flux-dilution factor $1/\sqrt{\mathcal V}$ for the second term and a factor $1/{\mathcal V}^2$ from Weyl rescaling to the 4d Einstein frame for both the first and second term. Thus, the total volume suppression for these two terms is stronger than in the aforementioned 4d EFT expectations. We discuss the underlying logic in detail, also in the gaugino condensation case, but fail to find a satisfactory explanation for the mismatch. While log-corrections to the Kähler potential may be responsible, these would have to be strong enough to affect the outcome of the LVS scheme at the ${\mathcal O}(1)$ level. What is worse, the origin of the required correction remains unclear.
发表机构
- Institute for Theoretical Physics, Heidelberg University（海德堡大学理论物理研究所）
- Department of Physics, Cornell University（康奈尔大学物理系）
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