Topologically twisted indices in five dimensions and holography

DOI10.1007/JHEP11(2018)119zbMATH Open1404.81232arXiv1808.06626MaRDI QIDQ1635222

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Publication date: 18 December 2018

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Abstract: We provide a formula for the partition function of five-dimensional $mathcalN=1$ gauge theories on $mathcal{M}_{4}imes{S}^1$, 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: $mathcalN=2$ SYM and the $mathrmUSp(2N)$ theory with $N_f$ flavors and an antisymmetric matter field. For $mathbb{P}^{1}imesmathbb{P}^{1}imes{S}^1$, which can be easily generalized to $Sigm{a}_{mathfrak{g}_2}imesSigm{a}_{mathfrak{g}_1}imes{S}^1$, we conjecture the form of the relevant saddle point at large $N$. The resulting partition function for $mathcalN=2$ SYM scales as $N^3$ and is in perfect agreement with the holographic results for domain walls in AdS${}_{7}imes{S}^4$. The large $N$ partition function for the $mathrmUSp(2N)$ 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.

Full work available at URL: https://arxiv.org/abs/1808.06626

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