Shifts of prepotentials (with an appendix by Michele Vergne)

Nekrasov, Nikita; Piazzalunga, Nicolo; Zabzine, Maxim

doi:10.21468/SciPostPhys.12.5.177

SciPost Physics

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.5.177
TI  - Shifts of prepotentials (with an appendix by Michele Vergne)
PY  - 2022/05/27
UR  - https://www.scipost.org/SciPostPhys.12.5.177
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 5
SP  - 177
A1  - Nekrasov, Nikita
AU  - Piazzalunga, Nicolo
AU  - Zabzine, Maxim
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.12.5.177,
	title={{Shifts of prepotentials (with an appendix by Michele Vergne)}},
	author={Nikita Nekrasov and Nicolo Piazzalunga and Maxim Zabzine},
	journal={SciPost Phys.},
	volume={12},
	pages={177},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.5.177},
	url={https://scipost.org/10.21468/SciPostPhys.12.5.177},
}

Cited by 4

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¹ ² ³ Nikita Nekrasov,
⁴ Nicolo Piazzalunga,
⁴ Maxim Zabzine

Funder for the research work leading to this publication

Knut och Alice Wallenbergs Stiftelse (Knut and Alice Wallenberg Foundation) (through Organization: Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation)