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

Katsuta Sakai

doi:10.1016/j.nuclphysb.2019.114801

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.

Highlights

To construct the theory of quantum gravity is one of the most important and difficult issues in the high-energy physics
We see that when we focus on the spin-s fields, the gauge symmetries and the torsion-free conditions leave the transverse components of the fields in the totally symmetric representation
We have studied whether the IIB matrix model contains higher spin fields in its degrees of freedom (DoF)

Summary

Introduction

To construct the theory of quantum gravity is one of the most important and difficult issues in the high-energy physics. They are solutions of the equations of motion in the model, and one can regard some parts of the fluctuations on them as the emergent gravity [14,15,16].2 Despite these variety of results, there is a room for discussion about the physical interpretation of the matrices. Looking back on the form of the IIB matrix model, it is the large-N reduction of super Yang-Mills theory Speaking, it implies that the DoF of the gauge field absorb their momenta. The U (N ) symmetry of the matrices are translated into a lot of symmetries of local fields, including diffeomorphism and local Lorentz symmetry These facts suggest that the matrix model in the operator interpretation contains the DoF to describe the spacetime and gravity.

A review of the operator interpretation of the matrix model

Higher spin gauge symmetries in the IIB matrix model

Equations of motion for higher spin fields

Summary and discussion