论文标题
5D SCFT的库仑分支上的分区功能和纤维操作员
Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
论文作者
论文摘要
我们研究5D $ \ MATHCAL {n} = 1 $超对称现场理论，封闭了五个manifolds $ \ Mathcal {M} _5 $，这是简单地连接的Kählerfour four four four four fout donaldsson-wister twist twist twist twist twist。我们提出了一种新方法，通过插入纤维操作员，在$ \ Mathcal {M} _5 $上计算超对称分区功能，该纤维操作员在4D拓扑现场理论中引入了$ \ Mathcal {M} _4 $的非平凡振动。我们在任何此类$ \ Mathcal {M} _5 $上确定所谓的库仑分支分区功能，该功能被认为是完整分区函数的holomorphic`nevelland'。我们精确地匹配了显式一环计算的低能有效现场理论方法，并在这种情况下讨论了非扰动5D BPS颗粒的效果。当$ \ Mathcal {M} _4 $是折磨时，我们还通过适当粘合Nekrasov分区功能来重建库仑分支分区功能。作为我们分析的副产品，我们为洛克哈特 - VAFA公式对五个球分区函数的有效性提供了有效的新证据。
We study 5d $\mathcal{N}=1$ supersymmetric field theories on closed five-manifolds $\mathcal{M}_5$ which are principal circle bundles over simply-connected Kähler four-manifolds, $\mathcal{M}_4$, equipped with the Donaldson-Witten twist. We propose a new approach to compute the supersymmetric partition function on $\mathcal{M}_5$ through the insertion of a fibering operator, which introduces a non-trivial fibration over $\mathcal{M}_4$, in the 4d topologically twisted field theory. We determine the so-called Coulomb branch partition function on any such $\mathcal{M}_5$, which is conjectured to be the holomorphic `integrand' of the full partition function. We precisely match the low-energy effective field theory approach to explicit one-loop computations, and we discuss the effect of non-perturbative 5d BPS particles in this context. When $\mathcal{M}_4$ is toric, we also reconstruct our Coulomb branch partition function by appropriately gluing Nekrasov partition functions. As a by-product of our analysis, we provide strong new evidence for the validity of the Lockhart-Vafa formula for the five-sphere partition function.
