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

• Main Authors: Junho Hong, James T. Liu
• Format: Article
• Language: English
• Published: SpringerOpen 2018-07-01
• Series: Journal of High Energy Physics
• Subjects: Supersymmetric Gauge Theory; AdS-CFT Correspondence; Conformal Field Theory
• Online Access: http://link.springer.com/article/10.1007/JHEP07(2018)018

Abstract We examine the topologically twisted index of N $$ \mathcal{N} $$ = 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/ℤ m  × ℤ n where N = mn. After summing over these sectors, the index can be expressed as the elliptic genus of a twodimensional N $$ \mathcal{N} $$ = (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 N $$ \mathcal{N} $$ = (0, 2) theory.