Space-Time and Matter in IIB Matrix Model - gauge symmetry and diffeomorphism -

TL;DR

This paper investigates how space-time and gauge symmetries emerge in the IIB matrix model, showing that low energy excitations propagate in a way consistent with local gauge invariance and diffeomorphism symmetry.

Contribution

It demonstrates the emergence of local SU(n) gauge symmetry and general covariance from the IIB matrix model through eigenvalue distributions and low energy excitations.

Findings

Low energy excitations propagate in the eigenvalue-based space-time.

Local SU(n) gauge symmetry arises from small eigenvalue clusters.

General covariance is realized in the low energy effective theory.

Abstract

We pursue the study of the type IIB matrix model as a constructive definition of superstring. In this paper, we justify the interpretation of space-time as distribution of eigenvalues of the matrices by showing that some low energy excitations indeed propagate in it. In particular, we show that if the distribution consists of small clusters of size $n$, low energy theory acquires local SU(n) gauge symmetry and a plaquette action for the associated gauge boson is induced, in addition to a gauge invariant kinetic term for a massless fermion in the adjoint representation of the SU(n). We finally argue a possible identification of the diffeomorphism symmetry with permutation group acting on the set of eigenvalues, and show that the general covariance is realized in the low energy effective theory even though we do not have a manifest general covariance in the IIB matrix model action.