The $\mathcal{N} = 2$ Prepotential and the Sphere Free Energy

Bernardo Zan; Daniel Z. Freedman; Silviu S. Pufu

The $\mathcal{N} = 2$ Prepotential and the Sphere Free Energy

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arxiv 2112.06931 v1 pith:4XKB2N5P submitted 2021-12-13 hep-th

Bernardo Zan , Daniel Z. Freedman , Silviu S. Pufu This is my paper · ORCID

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keywords energyfreemathcalsphereprepotentialsupergravitytheoriesboundary

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abstract

We study the mass-deformed sphere free energy of three-dimensional $\mathcal{N} = 2$ superconformal field theories with holographic duals. Building on previous observations, we conjecture a proportionality relation between the sphere free energy on the boundary and the prepotential of the four-dimensional $\mathcal{N} = 2$ supergravity theory in the bulk. We verify this formula by explicit computation in several examples of supergravity theories with vector multiplets and hypermultiplets.

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$\mathcal{N}=2$ Super Yang-Mills in AdS$_4$ and $F_{\text{AdS}}$-maximization
hep-th 2025-06 conditional novelty 7.0 of 10

A new maximization principle, F_AdS-maximization, selects boundary conditions for N=2 SYM in AdS4 and predicts a transition to a U(1)-Higgsed phase at strong coupling.

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