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

James T. Liu, Leopoldo A. Pando Zayas, Vimal Rathee, Wenli Zhao

TL;DR

This work investigates subleading corrections to microstate counting for magnetically charged AdS$_4$ black holes using the ABJM topologically twisted index and a one-loop gravity analysis. It combines a numerical field-theory study that finds a universal $-\tfrac{1}{2}\log N$ correction beyond the leading $N^{3/2}$ term with a gravity calculation focused on the near-horizon AdS$_2\times M_9$ geometry, which yields a $-2\log N$ correction from zero modes. The observed mismatch suggests limitations of the near-horizon/decomposition approach or of holographic renormalization for these backgrounds and motivates refined treatments of subleading corrections in AdS/CFT. The results point to potential revisions of the quantum entropy function framework for asymptotically AdS black holes and open directions to derive the subleading terms analytically and to study universality across related holographic pairs.

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.

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

TL;DR

This work investigates subleading corrections to microstate counting for magnetically charged AdS black holes using the ABJM topologically twisted index and a one-loop gravity analysis. It combines a numerical field-theory study that finds a universal correction beyond the leading term with a gravity calculation focused on the near-horizon AdS geometry, which yields a correction from zero modes. The observed mismatch suggests limitations of the near-horizon/decomposition approach or of holographic renormalization for these backgrounds and motivates refined treatments of subleading corrections in AdS/CFT. The results point to potential revisions of the quantum entropy function framework for asymptotically AdS black holes and open directions to derive the subleading terms analytically and to study universality across related holographic pairs.

Abstract

The topologically twisted index for ABJM theory with gauge group has recently been shown, in the large- limit, to reproduce the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS black holes. We numerically study the index beyond the large- limit and provide evidence that it contains a subleading logarithmic term of the form . 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.

Paper Structure

This paper contains 8 sections, 34 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. The topologically twisted index beyond the large-$N$ limit
  3. Evaluation of the index beyond the leading order in $N$
  4. Perilous $1/N$ expansion
  5. One-loop quantum supergravity
  6. The number and scalings of zero modes
  7. The logarithmic corrections
  8. Discussion

Figures (2)

  • Figure 1: The solution to the BAE for $\Delta_a=\{0.4,0.5,0.7,2\pi-1.6\}$ and $N=60$. The solid lines correspond to the leading order expression obtained in Benini:2015eyy.
  • Figure 2: The eigenvalue density $\rho(t)$ and the function $\delta v(t)$ for $\Delta_a=\{0.4,0.5,0.7,2\pi-1.6\}$ and $N=60$, compared with the leading order expression.