Subleading Microstate Counting in the Dual to Massive Type IIA
James T. Liu, Leopoldo A. Pando Zayas, Shan Zhou
TL;DR
The paper analyzes subleading corrections to the topologically twisted index of a massive IIA dual pair, focusing on a 3d ${\cal N}=2$ SU$(N)$ Chern-Simons-matter theory with adjoints whose leading ${N^{5/3}}$ growth matches magnetically charged AdS$_4\times S^6$ black holes. By combining numerical solutions of the Bethe Ansatz equations with a detailed analytic large-$N$ expansion, it shows cancellations of ${N\log N}$ and ${N^{1/3}\log N}$ terms, predicting the first subleading term to scale as ${N^{2/3}}$, and provides evidence for a universal $(g-1)(7/18)\log N$ coefficient tied to massless gravitational modes in the gravity dual. The analysis decomposes the index into determinant, chiral, and vector multiplet contributions, deriving subleading structures via Euler-Maclaurin, and discusses holographic implications, including one-loop gravity corrections and higher-derivative effects. These results advance precision tests of AdS$_4$/massive IIA duality and offer a field-theoretic prediction for gravitational quantum corrections to black hole entropy.
Abstract
We study the topologically twisted index of a certain Chern-Simons matter theory with $SU(N)$ level $k$ gauge group on a genus $g$ Riemann surface times a circle. For this theory it is known that the logarithm of the topologically twisted index grows as $N^{5/3}$ and that it matches the Bekenstein-Hawking entropy of certain magnetically charged asymptotically $AdS_4\times S^6$ black holes in massive type IIA supergravity. Through a combination of numerical and analytical techniques we study the subleading in $N$ structure. We demonstrate precise analytic cancellation of terms of orders $N\log\,N$ and $N^{1/3}\log N$ and show numerical cancellation for terms of order $N$. As a result, the first subleading correction is of order $N^{2/3}$. Furthermore, we provide evidence for the presence of a term of the form $(g-1)(7/18) \log \,N$ which constitutes a microscopic prediction for the one-loop contribution coming from the massless gravitational degrees of freedom in the massive IIA black hole.