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

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.

18 pages, 5 figures

References in corpus (4)

• Tensor model and dynamical generation of commutative nonassociative fuzzy spaces
• The lowest modes around Gaussian solutions of tensor models and the general relativity
• The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity
• Massive particles coupled with 2+1 dimensional gravity and noncommutative field theory

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• Numerical and analytical analyses of a matrix model with non-pairwise contracted indices
• A renormalization procedure for tensor models and scalar-tensor theories of gravity
• Emergent general relativity in the tensor models possessing Gaussian classical solutions
• An $OSp$ extension of Canonical Tensor Model
• Fuzzy spaces from tensor models, cyclicity condition, and n-ary algebras
• Constraint algebra of general relativity from a formal continuum limit of canonical tensor model