Solving the strongly coupled 2D gravity: 1. Unitary truncation and quantum group structure

Strongly compled gravity theories with Virasoro central charges equal to 7, 13, and 19 are shown to enjoy striking properties: at these values, the subset of chiral operators with real Virasoro-weights, acting on a subspaceH _phys, is shown to be closed by fusion and braiding, and to leave this subspace invariant. Moreover, the representation of the Virasoro algebra becomes unitary when it is restricted toH _phys. Strongly coupled 2D gravity withC _grav=7, 13, or 19 may thus be naturally truncated obtaining a consistent conformal theory (this result is similar to the truncation that occurs forC=1–6(p–p) ²/pp withp andp integers, where only a finite number of primary fields remains, as is well known in rational theories). The proof of this unitary truncation theorem, already summarized in a recent letter, is fully described here.