The N $$ \mathcal{N} $$ = 2 prepotential and the sphere free energy

Abstract

Abstract

We study the mass-deformed sphere free energy of three-dimensional

N

$$ \mathcal{N} $$ = 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

N

$$ \mathcal{N} $$ = 2 supergravity theory in the bulk. We verify this formula by explicit computation in several examples of supergravity theories with vector multiplets and hypermultiplets.