Higher-spin kinematics & no ghosts on quantum space-time in Yang–Mills matrix models

A classification of bosonic on- and off-shell modes on a cosmological quantum space-time solution of the IIB matrix model is given, which leads to a higher-spin gauge theory. In particular, the no-ghost-theorem is established. The physical on-shell modes consist of $2$ towers of higher-spin modes, which are effectively massless but include would-be massive degrees of freedom. The off-shell modes consist of $4$ towers of higher-spin modes, one of which was missing previously. The noncommutativity leads to a cutoff in spin, which disappears in the semi-classical limit. An explicit basis allows to obtain the full propagator, which is governed by a universal effective metric. The physical metric fluctuations arise from would-be massive $\operatorname{spin}2$ modes, which were previously shown to include the linearized Schwarzschild solution. Due to the maximal supersymmetry of the IIB model, this is expected to define a consistent quantum theory in $3+1$ dimensions, which includes gravity.

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Published 12 April 2022