Topologically twisted indices in five dimensions and holography

Abstract

Abstract We provide a formula for the partition function of five-dimensional $$ \mathcal{N}=1 $$ N = 1 gauge theories on ℳ4 × S 1, topologically twisted along ℳ4 in the presence of general background magnetic fluxes, where ℳ4 is a toric Kähler 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: $$ \mathcal{N} $$ N = 2 SYM and the USp(2N) theory with N f flavors and an antisymmetric matter field. For ℙ1×ℙ1×S 1, which can be easily generalized to $$ {\varSigma}_{{\mathfrak{g}}_2}\times {\varSigma}_{{\mathfrak{g}}_1}\times {S}^1 $$ Σ g 2 × Σ g 1 × S 1 , we conjecture the form of the relevant saddle point at large N. The resulting partition function for $$ \mathcal{N} $$ N = 2 SYM scales as N 3 and is in perfect agreement with the holographic results for domain walls in AdS7 × 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.