Abstract
We investigate the large-N asymptotics of the topologically twisted index of mathcal{N} = 4 SU(N) Super-Yang-Mills (SYM) theory on T2 × S2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of mathcal{N} = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual mathcal{N} = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index.
Highlights
Counting has been done by investigating asymptotic symmetries of the near-horizon limit of a 3d Bañados-Teitelboim-Zanelli (BTZ) black hole [5, 6]
We investigate the large-N asymptotics of the topologically twisted index of N = 4 SU(N ) Super-Yang-Mills (SYM) theory on T 2 × S2 and provide its holographic interpretation based on the black hole Farey tail [1]
In this approach initiated in [7], the Bekenstein-Hawking entropy of a supersymmetric AdS black hole is matched with the logarithm of the microcanonical partition function (=the number of microstates) of a dual superconformal field theory (SCFT) on the conformal boundary of the bulk, in the large-N limit where N denotes the rank of the gauge group
Summary
The BA formula (2.9) does not clarify ‘relevant’ BAE solutions that contribute to the twisted index. The contour C is introduced rather implicitly in (2.1) to capture the JK residues, and it is not trivial to decide if a given BAE solution truly contributes to the twisted index through the BA formula (2.9). The contribution from various standard BAE solutions to the twisted index through the BA formula (2.9) has been written explicitly in [31]. We have introduced a shorthand notation for the Jacobian determinant of a standard BAE solution as H{m,n,r}(τ, ∆a) ≡ H({ui}{m,n,r}; τ, ∆a). The expressions (2.14) and (2.22) are equivalent to each other and give the contribution to the twisted index from a standard BAE solution — labelled by {m, n, r} as (2.11) —. We investigate the large-N asymptotics of a particular standard contribution Z{m,n,r} (2.14), or (2.22), that composes the total standard contribution Zst through (2.13b)
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call