From Coxeter higher-spin theories to strings and tensor models

A new class of higher-spin gauge theories associated with various Coxeter groups is proposed. The emphasize is on the Bp-models. The cases of B1 and its infinite graded-symmetric product sym (×B1)∞ correspond to the usual higher-spin theory and its multi-particle extension, respectively. The multi-particle B2-higher-spin theory is conjectured to be associated with String Theory. Bp-higher-spin models with p > 2 are anticipated to be dual to the rank-p boundary tensor sigma-models. Bp higher-spin models with p ≥ 2 possess two coupling constants responsible for higher-spin interactions in AdS background and stringy/tensor effects, respectively. The brane-like idempotent extension of the Coxeter higher-spin theory is proposed allowing to unify in the same model the fields supported by space-times of different dimensions. Consistency of the holographic interpretation of the boundary matrix-like model in the B2-higher-spin model is shown to demand N ≥ 4 SUSY, suggesting duality with the N = 4 SYM upon spontaneous breaking of higher-spin symmetries. The proposed models are shown to admit unitary truncations.