Gauge fixing in the tensor model and emergence of local gauge symmetries

TL;DR

This paper demonstrates that local gauge symmetries, akin to those in general relativity, can emerge in tensor models through BRS gauge fixing, with ghost modes matching reparametrization ghosts.

Contribution

It applies BRS gauge fixing to tensor models and shows the emergence of massless ghost modes identical to those in general relativity.

Findings

Massless ghost trajectories are identified in the tensor model.

Ghost modes match reparametrization ghosts in general relativity.

Supports the idea of emergent gauge symmetries in tensor models.

Abstract

The tensor model can be regarded as theory of dynamical fuzzy spaces, and gives a way to formulate gravity on fuzzy spaces. It has recently been shown that the low-lying fluctuations around the Gaussian background solutions in the tensor model agree correctly with the metric fluctuations on the flat spaces with general dimensions in the general relativity. This suggests that the local gauge symmetry (the symmetry of local translations) is also emergent around these solutions. To systematically study this possibility, I apply the BRS gauge fixing procedure to the tensor model. The ghost kinetic term is numerically analyzed, and it has been found that there exist some massless trajectories of ghost modes, which are clearly separated from the other higher ghost modes. Comparing with the corresponding BRS gauge fixing in the general relativity, these ghost modes forming the massless trajectories in the tensor model are shown to be identical to the reparametrization ghosts in the general relativity.