# Witten index of BMN matrix quantum mechanics

**Authors:** Chi-Ming Chang  
**arXiv:** [2404.18442](https://arxiv.org/abs/2404.18442)  
**Date:** 2024-04-29  
**Summary page:** https://www.summarizepaper.com/en/paper/2404.18442v1/

## Key points

- Chi-Ming Chang explores the Witten index of Berenstein-Maldacena-Nastase matrix quantum mechanics.
- The Witten index is used for counting ground states and determining differences between bosonic and fermionic BPS states with non-zero spins.
- Calculation establishes a lower bound on entropy and provides insight into system properties.
- Significant finding: Entropy exhibits $N^2$ growth, impacting predictions of BPS black holes in M-theory.
- Black holes are expected to be asymptotic to plane wave geometries, enhancing understanding of complex structures in theoretical physics.
- Connection between Witten index in infinite $N$ limit and superconformal index linked to Aharony-Bergman-Jafferis-Maldacena theory is explored.
- Study reveals deeper connections between different theoretical frameworks and offers insights into governing principles of these systems.

## Summary

In their paper titled "Witten Index of BMN Matrix Quantum Mechanics," Chi-Ming Chang explores the Witten index of Berenstein-Maldacena-Nastase matrix quantum mechanics. The Witten index is a valuable tool for counting ground states and determining the disparity between bosonic and fermionic BPS states with non-zero spins. This calculation not only provides insight into the system's properties but also establishes a lower bound on entropy. One significant finding highlighted in the study is the $N^2$ growth exhibited by entropy, which has implications for predicting BPS black holes within M-theory. These black holes are expected to be asymptotic to plane wave geometries, enriching our understanding of these complex structures in theoretical physics. Furthermore, Chang delves into a fascinating connection between the Witten index in the infinite $N$ limit and the superconformal index associated with Aharony-Bergman-Jafferis-Maldacena theory. By exploring this relationship, the study sheds light on deeper connections between different theoretical frameworks and provides valuable insights into the underlying principles governing these systems. Overall, Chang's research offers a comprehensive analysis of the Witten index within matrix quantum mechanics, uncovering intricate relationships and implications for fundamental concepts in theoretical physics.