Witten index of BMN matrix quantum mechanics

TL;DR

This paper calculates the Witten index of BMN matrix quantum mechanics, revealing insights into BPS states, black hole entropy, and connections to superconformal indices, thus advancing understanding of M-theory and gauge/gravity duality.

Contribution

It provides the first detailed computation of the Witten index for BMN matrix quantum mechanics, linking it to black hole entropy and superconformal indices.

Findings

Witten index indicates an $N^2$ entropy growth.

Predicts the existence of BPS black holes in M-theory.

Establishes a relation between the index and superconformal index.

Abstract

We compute the Witten index of the Berenstein-Maldacena-Nastase matrix quantum mechanics, which counts the number of ground states as well as the difference between the numbers of bosonic and fermionic BPS states with nonzero spins. The Witten index sets a lower bound on the entropy, which exhibits an $N^2$ growth that predicts the existence of BPS black holes in M-theory, asymptotic to the plane wave geometry. We also discuss a relation between the Witten index in the infinite $N$ limit and the superconformal index of the Aharony-Bergman-Jafferis-Maldacena theory.