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

Abstract

We examine the topologically twisted index of 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 = (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 = (0, 2) theory.

Black hole microstate counting in Type IIB from 5d SCFTs

“…However, the gauge fluxes were set to zero from the outset in the proposal of[30]. The results were found to disagree with the supergravity computations in Type IIA, and we find similar mismatches with Type IIB supergravity for the dualities considered here 11. Notice that the exponent of the determinant factor is changed due to the addition of the Jabobian for the change of variables.…”

“…The topologically twisted index [1,2] of the ABJM theory [3] has been shown to count the microstates of magnetically charged AdS 4 black holes [4] in the holographically dual gravitational theory in [5,6]. This was soon generalized to other three-and four-dimensional gauge theories [7][8][9][10][11][12][13][14][15][16][17][18], 1 as well as the five-dimensional USp(2N ) ("Seiberg") theories which can be realized by D4-D8-O8 systems and have holographic duals in massive type IIA supergravity [27][28][29]. Specifically, the topologically twisted index of N = 1 gauge theories in five dimensions is given by the partition function on M 4 × S 1 with a partial topological twist on M 4 .…”

Microstates of rotating AdS5 strings

“…As shown in [34], this is actually a solution to the Bethe equations for arbitrary β. The unrefined twisted index in the Cardy limit and at finite N can then be compactly written as [4] log…”

Microstate counting via Bethe Ansätze in the 4d $$ \mathcal{N} $$ = 1 superconformal index

“…It is natural to make an attempt with a direct generalization of the type of solution encountered in [8], namely: u ab ij = τ N (i a − i b ) and λ a = (N − 1) 2. These solutions appeared first in [27] while evaluating the topologically twisted of 4d N = 1 theories on T 2 × S 2 in the high temperature limit; it was later shown in [28] that such configuration provides an exact solution on the Bethe-Ansatz equations.…”