Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity

TL;DR

This paper investigates the topologically twisted index of ABJM theory beyond the large-N limit, revealing a subleading logarithmic term and exploring its holographic dual, highlighting discrepancies with near horizon state contributions.

Contribution

It provides the first numerical evidence of subleading logarithmic corrections in the index beyond large-N and examines their holographic interpretation.

Findings

Identifies a -1/2 log N correction in the index beyond large-N

Holographic one-loop calculations produce the logarithmic term

Discrepancy between near horizon state contributions and field theory results

Abstract

The topologically twisted index for ABJM theory with gauge group $U(N)_k \times U(N)_{-k}$ has recently been shown, in the large-$N$ limit, to reproduce the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS$_4$ black holes. We numerically study the index beyond the large-$N$ limit and provide evidence that it contains a subleading logarithmic term of the form $-1/2\log N$. On the holographic side, this term naturally arises from a one-loop computation. However, we find that the contribution coming from the near horizon states does not reproduce the field theory answer. We give some possible reasons for this apparent discrepancy.