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Equivariant localization and gluing rules in 4d mathcal{N}=2 higher derivative supergravity
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Equivariant localization and gluing rules in 4d mathcal{N}=2 higher derivative supergravity
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We complete the proof of the conjecture in arXiv:2111.06903 regarding the form of gravitational building blocks in higher derivative supergravity and examine the related gluing rules. The derivation, based on certain assumptions, combines the BVAB equivariant localization formula (on non-compact spaces) and the direct evaluation of the action on the Omega background in AdS$_4$, arXiv:2212.10590. Utilizing the superconformal gravity formalism and avoiding equations of motion ensures our results are valid at any perturbative order in the Newton constant. As an application, we illustrate the holographic predictions for supersymmetric M2-brane partition functions. We conclude with a to-do list of related calculations in effective supergravity and string theory, aiming for full quantum control of BPS backgrounds.
Forward citations
Cited by 3 Pith papers
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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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Indices of M5 and M2 branes at finite $N$ from equivariant volumes, and a new duality
Finite-N indices for M5- and M2-branes are expressed via the same equivariant characteristic classes, generalizing M2/M5 duality through geometry exchange.
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Equivariant localization for higher derivative supergravity
Equivariantly closed forms in D=4 N=2 conformal supergravity allow closed-form supersymmetric observables in higher derivative theories without solving equations of motion.
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