标题： 弦理论中的小动能混合 显示英文标题

标题： Small Kinetic Mixing in String Theory

摘要： 不同$U(1)$因子的规范场之间的动能混合是在4d有效场论中被广泛研究的现象。 在具有来自隔离D膜区的$U(1)$的弦紧化中，动能混合成为对一个现象学重要有效场论算符进行紫外预测的关键目标。 令人惊讶的是，在许多情况下由于非平凡的抵消作用，动能混合是不存在的。 特别是，在IIB型弦理论中D3-D3的动能混合为零，而D3-反D3的混合则不为零。 这既来自于环面上的精确共形场论计算，也来自于十维超引力的一阶分析，在其中关键的抵消作用发生在$C_2$和$B_2$贡献之间。 我们采用后者的方法，在现实的卡拉比-丘空间设置中唯一可用的方法，通过包括膜作用量的次主导项并允许$C_0$非零，来提高精度。 精确的抵消仍然存在，我们认为这是由$SL(2,\mathbb{R})$自对偶性导致的结果。 我们注意到，在D3膜上的$B_2C_2$项在最近的文献中常常被忽略，但它是得到正确零结果所必需的。 最后，允许存在$SL(2,\mathbb{R})$破坏通量的情况下，D3-膜之间的动力学混合在体积抑制的层次上出现。我们提供了基本的显式公式，包括动力学和磁性混合，将对现象学相关、更复杂的情况的研究留待未来进行。我们还注意到，用4d超引力描述我们的结果似乎需要高阶导数项——这是一个值得进一步研究的问题。 显示英文摘要

摘要： Kinetic mixing between gauge fields of different $U(1)$ factors is a well-studied phenomenon in 4d EFT. In string compactifications with $U(1)$s from sequestered D-brane sectors, kinetic mixing becomes a key target for the UV prediction of a phenomenologically important EFT operator. Surprisingly, in many cases kinetic mixing is absent due to a non-trivial cancellation. In particular, D3-D3 kinetic mixing in type-IIB vanishes while D3-anti-D3 mixing does not. This follows both from exact CFT calculations on tori as well as from a leading-order 10d supergravity analysis, where the key cancellation is between the $C_2$ and $B_2$ contribution. We take the latter approach, which is the only one available in realistic Calabi-Yau settings, to a higher level of precision by including sub-leading terms of the brane action and allowing for non-vanishing $C_0$. The exact cancellation persists, which we argue to be the result of $SL(2,\mathbb{R})$ self-duality. We note that a $B_2C_2$ term on the D3-brane, which is often missing in the recent literature, is essential to obtain the correct zero result. Finally, allowing for $SL(2,\mathbb{R})$-breaking fluxes, kinetic mixing between D3-branes arises at a volume-suppressed level. We provide basic explicit formulae, both for kinetic as well as magnetic mixing, leaving the study of phenomenologically relevant, more complex situations for the future. We also note that describing our result in 4d supergravity appears to require higher-derivative terms - an issue which deserves further study.