Hong, Junho

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

We examine the topologically twisted index of $ \mathcal{N} $ = 4 super-Yang-Mills with gauge group SU(N ) on T 2 × S 2 , and demonstrate that it receives contributions from multiple sectors corresponding to the freely acting orbifolds T 2 /$ \mathbb{Z} $m × $ \mathbb{Z} $n 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 S 2 . 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.