论文标题
5D BPS箭和KK塔
5D BPS Quivers and KK Towers
论文作者
论文摘要
我们探索了d = 5理论的BPS颤动，在一个圆圈上被压缩，并在局部Calabi-yau上进行了几何设计3倍，为此，许多已知的机器导致（精制）索引由于超电势的微调而失败。对于阿贝利安（Abelian）的颤动，计数减少到了几何形状，但是在技术上具有挑战性的$ l^2 $共同体学被证明对于明智的BPS光谱是必不可少的。我们提供了一种数学定理来纠正困难，但是对于非亚伯式纪念物而言，协同学方法本身失败了，因为相关的波形本质上是理论上的。对于量规多重的漫画部分（没有墙壁交叉），我们求助于D0图片并重建整个KK塔。我们还使用多中心的库仑例程进行数值检查，并在颤抖的不变性上有一个简单的假设，并将其扩展到弱耦合室中的电BPS状态。我们对已知的Donaldson-Thomas不变性以及如何从中读取$ l^2 $ index的评论。
We explore BPS quivers for D=5 theories, compactified on a circle and geometrically engineered over local Calabi-Yau 3-folds, for which many of known machineries leading to (refined) indices fail due to the fine-tuning of the superpotential. For Abelian quivers, the counting reduces to a geometric one, but the technically challenging $L^2$ cohomology proved to be essential for sensible BPS spectra. We offer a mathematical theorem to remedy the difficulty, but for non-Abelian quivers, the cohomology approach itself fails because the relevant wavefunctions are inherently gauge-theoretical. For the Cartan part of gauge multiplets, which suffers no wall-crossing, we resort to the D0 picture and reconstruct entire KK towers. We also perform numerical checks using a multi-center Coulombic routine, with a simple hypothesis on the quiver invariants, and extend this to electric BPS states in the weak coupling chamber. We close with a comment on known Donaldson-Thomas invariants and on how $L^2$ index might be read off from these.
