Topologically twisted indices in five dimensions and holography

Understand

We provide a formula for the partition function of five-dimensional $\mathcal{N}=1$ gauge theories on $\mathcal{M}_4 \times S^1$, topologically twisted along $\mathcal{M}_4$ in the presence of general background magnetic fluxes, where $\mathcal{M}_4$ is a toric K\"ahler 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: $\mathcal{N}=2$ SYM and the $\mathrm{USp}(2N)$ theory with $N_f$ flavors and an antisymmetric matter field.