Topological wave functions and the 4D-5D lift

Details Topological wave functions and the 4D-5D lift Topological wave functions and the 4D-5D lift

2008-03-05

arxiv.org/abs/0803.0562v2

JHEP0807:087,2008

Physics

High Energy Physics

High Energy Physics - Theory

minor corrections, version to appear in JHEP

Scientific paper

10.1088/1126-6708/2008/07/087

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 K\"ahler 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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