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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Zan, B., Freedman, D.Z. & Pufu, S.S. The \( \mathcal{N} \) = 2 prepotential and the sphere free energy. J. High Energ. Phys. 2022, 45 (2022). https://doi.org/10.1007/JHEP06(2022)045
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DOI: https://doi.org/10.1007/JHEP06(2022)045