Shifts of prepotentials

Nikita Nekrasov, Nicolo Piazzalunga, Maxim Zabzine, Michèle Vergne

Research output: Contribution to journalArticlepeer-review


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 Kähler 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 Kähler 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.

Original languageEnglish
Article number177
JournalSciPost Physics
Issue number5
Publication statusPublished - 2022


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