Shifts of prepotentials (with an appendix by Michele Vergne)
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.
Keywords
Cite
@article{arxiv.2111.07663,
title = {Shifts of prepotentials (with an appendix by Michele Vergne)},
author = {Nikita Nekrasov and Nicolo Piazzalunga and Maxim Zabzine},
journal= {arXiv preprint arXiv:2111.07663},
year = {2022}
}
Comments
Added appendix by M.Vergne, which provides alternative proof of shift equation