Shifts of prepotentials (with an appendix by Michele Vergne)
Nikita Nekrasov, Nicolo Piazzalunga, Maxim Zabzine
SciPost Phys. 12, 177 (2022) · published 27 May 2022
- doi: 10.21468/SciPostPhys.12.5.177
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Abstract
We study the dynamics of supersymmetric theories in five dimensions obtained by compactifications of M-theory on a Calabi-Yau threefold X. For a compact X, this is determined by the geometry of X, in particular the Kahler class dependence of the volume of X determines the effective couplings of vector multiplets. Rigid supersymmetry emerges in the limit of divergent volume, prompting the study of the structure of Duistermaat-Heckman formula and its generalizations for non-compact toric Kahler manifolds. Our main tool is the set of finite-difference equations obeyed by equivariant volumes and their quantum versions. We also discuss a physical application of these equations in the context of seven-dimensional gauge theories, extending and clarifying our previous results. The appendix by M. Vergne provides an alternative local proof of the shift equation.
Cited by 4
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 3 Nikita Nekrasov,
- 4 Nicolo Piazzalunga,
- 4 Maxim Zabzine
- 1 Skolkovo Institute of Science and Technology [Skoltech]
- 2 Stony Brook University [SUNY Stony Brook]
- 3 Kharkevich Institute / Institute for Information Transmission Problems
- 4 Uppsala universitet / Uppsala University