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arXiv 2103.07472hep-th
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五次Calabi-Yau流形上的模依赖KK塔和沼泽地距离猜想

Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold

Anthony Ashmore, Fabian Ruehle

摘要:

我们利用数值方法得到了单参数五次Calabi-Yau流形族的模相关Calabi-Yau度规,并由此得到了模相关的Kaluza-Klein态的质量塔.然后,我们计算测地线距离在他们的凯勒和复杂的结构模空间使用精确表达式从镜像对称,近似表达式和数值方法,并比较结果。最后,我们将质量谱的模依赖性拟合到测地距离,以获得状态变为指数光的速率。结果确实是一阶的,正如沼泽地距离猜想所暗示的那样。我们还观察到的本征值谱的水平交叉,并发现在小的不可约表示的对称群的状态往往变得轻于在较大的不可约表示的状态。

英文摘要:

We use numerical methods to obtain moduli-dependent Calabi-Yau metrics and from them the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds. We then compute geodesic distances in their Kähler and complex structure moduli space using exact expressions from mirror symmetry, approximate expressions, and numerical methods and compare the results. Finally, we fit the moduli-dependence of the massive spectrum to the geodesic distance to obtain the rate at which states become exponentially light. The result is indeed of order one, as suggested by the swampland distance conjecture. We also observe level-crossing in the eigenvalue spectrum and find that states in small irreducible representations of the symmetry group tend to become lighter than states in larger irreducible representations.

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