# The topologically twisted index of $$\mathcal{N}$$ = 4 super-Yang-Mills on T 2 × S2 and the elliptic genus

Journal of High Energy Physics, Jul 2018

Abstract We examine the topologically twisted index of $$\mathcal{N}$$ = 4 super-Yang-Mills with gauge group SU(N ) on T 2×S2, and demonstrate that it receives contributions from multiple sectors corresponding to the freely acting orbifolds T2/ℤm × ℤn where N = mn. After summing over these sectors, the index can be expressed as the elliptic genus of a twodimensional $$\mathcal{N}$$ = (0, 2) theory resulting from Kaluza-Klein reduction on S2. This provides an alternate path to the ‘high-temperature’ limit of the index, and confirms the connection to the right-moving central charge of the $$\mathcal{N}$$ = (0, 2) theory.

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Junho Hong, James T. Liu. The topologically twisted index of $$\mathcal{N}$$ = 4 super-Yang-Mills on T 2 × S2 and the elliptic genus, Journal of High Energy Physics, 2018, 18, DOI: 10.1007/JHEP07(2018)018