# On the transverse M5-branes in matrix theory

## TL;DR

This paper provides evidence that transverse M5-branes in M-theory are represented within the plane wave matrix model by analyzing eigenvalue distributions in the strong coupling limit.

## Contribution

It demonstrates, through localization and eigenvalue analysis, that spherical M5-branes are captured by the matrix model in the strong coupling regime.

## Key findings

- Eigenvalue density matches M5-brane shape in decoupling limit
- Supports the idea that M5-branes are contained in matrix theory
- Provides evidence for second quantization of M-theory

## Abstract

It has been a long-standing problem how the transverse M5-branes are described in the matrix-model formulations of M-theory. We consider this problem for M-theory on the maximally supersymmetric pp-wave geometry, which admits transverse spherical M5-branes with zero light-cone energy. By using the localization, we directly analyze the strong coupling region of the corresponding matrix theory called the plane wave matrix model (PWMM). Under the assumption that the low energy modes of the scalar fields in PWMM become mutually commuting in the strong coupling region, we show that the eigenvalue density of the $SO(6)$ scalars in the low energy region exactly agrees with the shape of the spherical M5-branes in the decoupling limit. This result gives a strong evidence that the transverse M5-branes are indeed contained in the matrix theory and the theory realizes a second quantization of the M-theory.