Giant Graviton and Quantum Stability in Matrix Model on PP-wave Background

TL;DR

This paper investigates classical solutions in the BMN matrix model, focusing on giant gravitons and their quantum stability, along with other configurations like non-supersymmetric fuzzy spheres and oscillating gravitons.

Contribution

It provides a detailed analysis of classical solutions, including supersymmetric and non-supersymmetric fuzzy spheres, and demonstrates quantum stability of the giant graviton in the matrix model.

Findings

Supersymmetric fuzzy sphere (giant graviton) is quantum mechanically stable.

Non-supersymmetric fuzzy sphere is shown to be unstable.

Oscillating gravitons reduce to supergravitons as mu approaches zero.

Abstract

We study classical solutions in Berenstein-Maldacena-Nastase (BMN) matrix model. A supersymmetric (1/2 BPS) fuzzy sphere is one of the classical solutions and corresponds to a giant graviton. We also consider other classical solutions, such as non-supersymmetric fuzzy sphere and harmonic oscillating gravitons. Some properties of oscillating gravitons are discussed. In particular, oscillating gravitons turn into usual supergravitons in the limit mu -> 0. Moreover, we calculate the one-loop effective action around the supersymmetric fuzzy sphere by the use of the background field method and show the quantum stability of the giant graviton. Also, the instability of the non-supersymmetric fuzzy sphere is proven.