Topologically twisted indices in five dimensions and holography

We provide a formula for the partition function of five-dimensional N = 1 gauge theories on M-4 x S-1, topologically twisted along M-4 in the presence of general background magnetic fluxes, where M-4 is a toric Kahler manifold. The result can be expressed as a contour integral of the product of copies of the K-theoretic Nekrasov's partition function, summed over gauge magnetic fluxes. The formula generalizes to five dimensions the topologically twisted index of three- and four-dimensional field theories. We analyze the large N limit of the partition function and some related quantities for two theories: N = 2 SYM and the USp(2N) theory with N-f flavors and an antisymmetric matter field. For P-1 x P-1 x S-1, which can be easily generalized to Sigma(g2) x Sigma(g1) x S-1, we conjecture the form of the relevant saddle point at large N. The resulting partition function for N = 2 SYM scales as N-3 and is in perfect agreement with the holographic results for domain walls in AdS7 x S-4. The large N partition function for the USp(2N) theory scales as N-5/2 and gives a prediction for the entropy of a class of magnetically charged black holes in massive type IIA supergravity.