# A note on higher spin symmetry in the IIB matrix model with the operator interpretation

## TL;DR

This paper investigates higher spin gauge symmetries within the IIB matrix model interpreted as differential operators on curved spacetimes, revealing the emergence of higher spin fields and their gauge invariances.

## Contribution

It demonstrates how higher spin gauge symmetries can be realized in the IIB matrix model through auxiliary fields and identifies the physical degrees of freedom as transverse components of a generalized curvature tensor.

## Key findings

- Higher spin gauge symmetries are present with auxiliary fields.
- Physical degrees of freedom are transverse components of a symmetric tensor.
- The identified field generalizes the concept of curvature, not the Fronsdal field.

## Abstract

We study the IIB matrix model in an interpretation where the matrices are differential operators defined on curved spacetimes. In this interpretation, coefficients of higher derivative operators formally appear to be massless higher spin fields. In this paper, we examine whether the unitary symmetry of the matrices includes appropriate higher spin gauge symmetries. We focus on fields that are bosonic and relatively simple in the viewpoint of the representation of Lorentz group. We find that the additional auxiliary fields need to be introduced in order to see the higher spin gauge symmetries explicitly. At the same time, we point out that a part of these extra fields are gauged-away, and the rest of part can be written in terms of a totally symmetric tensor field. The transformation to remove its longitudinal components exists as well. As a result, we observe that the independent physical DoF are the transverse components of that symmetric field, and that the theory describes the corresponding higher spin field. We also find that the field is not the Fronsdal field, rather the generalization of curvature.