Symmetry breaking in twisted Eguchi-Kawai models

We present numerical evidence for the spontaneous breaking of the ZN4 symmetry of four-dimensional twisted Eguchi-Kawai models with SU(N) gauge group and symmetric twist, for sufficiently large N. We find that for N⩾100 this occurs for a wide range of bare couplings. Moreover for N⩽144, where we have been able to perform detailed calculations, there is no window of couplings where the physically interesting confined and deconfined phases appear in the reduced model. We provide a possible interpretation for this in terms of generalised 'fluxon' configurations. We discuss the implications of our findings for the validity and utility of space-time reduced models as N→∞.