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arXiv 2011.00024hep-th
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4d N=1无限距离极限下的量子修正与弱引力猜想

Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture

Daniel Klaewer, Seung-Joo Lee, Timo Weigand, Max Wiesner

摘要:

我们在量子引力猜想的背景下研究了具有$N=1$超对称性的四维理论中的量子修正。根据突现弦猜想,量子引力中的无限距离限制要么导致理论的解压缩,要么导致弱耦合的弦论。我们验证了这一猜想的框架下的$N=1$超对称F-理论紧化的四维,包括微扰$α'$以及非微扰修正。在经典水平上证明了紧急临界弦的唯一性之后,我们证明了量子修正恰好阻碍了紧急临界弦的尺度在参数上低于卡鲁扎-克莱因尺度的那些极限。相比之下,渐近无张力弦的张力处于卡鲁扎-克莱因尺度的极限是不受阻碍的。本文的第二部分研究了远离严格弱耦合极限的量子修正对弱引力猜想的影响。我们建议,规范阈值修正和质量重整化效应修改超极值约束在四维。对于F-理论中的无限距离极限,经典超极值界一般由突现杂化弦激发塔中的子格态满足。通过匹配F理论的$α'$修正到对偶杂种优势理论的规范阈值修正,我们预测了这个塔的质量必须如何重新归一化,以便弱引力猜想在量子水平上成立。

英文摘要:

We study quantum corrections in four-dimensional theories with $N=1$ supersymmetry in the context of Quantum Gravity Conjectures. According to the Emergent String Conjecture, infinite distance limits in quantum gravity either lead to decompactification of the theory or result in a weakly coupled string theory. We verify this conjecture in the framework of $N=1$ supersymmetric F-theory compactifications to four dimensions including perturbative $α'$ as well as non-perturbative corrections. After proving uniqueness of the emergent critical string at the classical level, we show that quantum corrections obstruct precisely those limits in which the scale of the emergent critical string would lie parametrically below the Kaluza-Klein scale. Limits in which the tension of the asymptotically tensionless string sits at the Kaluza-Klein scale, by contrast, are not obstructed. In the second part of the paper we study the effect of quantum corrections for the Weak Gravity Conjecture away from the strict weak coupling limit. We propose that gauge threshold corrections and mass renormalisation effects modify the super-extremality bound in four dimensions. For the infinite distance limits in F-theory the classical super-extremality bound is generically satisfied by a sublattice of states in the tower of excitations of an emergent heterotic string. By matching the F-theory $α'$ corrections to gauge threshold corrections of the dual heterotic theory we predict how the masses of this tower must be renormalised in order for the Weak Gravity Conjecture to hold at the quantum level.

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