拓扑波函数与四维-五维升力
Topological wave functions and the 4D-5D lift
摘要：
在“魔术"N=2超引力理论的背景下，我们从4D-5D升力的角度重新讨论了拓扑弦振幅所满足的全纯反常方程。特别是，我们解释的Gopakumar-Vafa关系之间的5D黑洞简并和拓扑弦振幅的结果，从4D到5D收费的正则变换。此外，我们利用已知的5D黑洞的Bekenstein-Hawking熵来限制拓扑波函数在有限拓扑耦合但大Kähler类下的渐近行为.在这个过程中，一些微妙的关系之间的5D黑洞简并和拓扑弦振幅被发现，但没有解决。最后，我们将这些考虑扩展到拓扑弦振幅的假定单参数推广，并将正则变换确定为3D对偶群内的Weyl反射。
英文摘要：
We revisit the holomorphic anomaly equations satisfied by the topological string amplitude from the perspective of the 4D-5D lift, in the context of ''magic'' N=2 supergravity theories. In particular, we interpret the Gopakumar-Vafa relation between 5D black hole degeneracies and the topological string amplitude as the result of a canonical transformation from 4D to 5D charges. Moreover we use the known Bekenstein-Hawking entropy of 5D black holes to constrain the asymptotic behavior of the topological wave function at finite topological coupling but large Kähler classes. In the process, some subtleties in the relation between 5D black hole degeneracies and the topological string amplitude are uncovered, but not resolved. Finally we extend these considerations to the putative one-parameter generalization of the topological string amplitude, and identify the canonical transformation as a Weyl reflection inside the 3D duality group.
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