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Shifts of prepotentials (with an appendix by Michele Vergne)
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Shifts of prepotentials (with an appendix by Michele Vergne)
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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.
Forward citations
Cited by 3 Pith papers
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Odd-Dimensional Localization in Supergravity
The on-shell action of odd-dimensional supergravity with Chern-Simons terms localizes to fixed points via relative equivariant cohomology, yielding a universal formula matching M5-brane and black ring physics.
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Airy functions from quantum M-theory
Airy function partition functions for M2-brane theories are derived from relative equivariant localization of quantum M-theory, with the 11D Chern-Simons term giving the cubic term and X₈ giving the charge shift.
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Airy functions from quantum M-theory
Relative equivariant localization of quantum M-theory reproduces the Airy partition functions of ABJM and toric Calabi-Yau M2-brane theories, up to prefactor and non-perturbative corrections.
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