arXiv:1804.06520v3 [hep-th] 16 Aug 2018 FIAN/TD/02-18 From Coxeter Higher-Spin Theories to Strings and Tensor Models M.A. Vasiliev I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute, Leninsky prospect 53, 119991, Moscow, Russia To my father Abstract A new class of higher-spin gauge theories associated with various Coxeter groups is proposed.The emphasize is on theBp–models.The cases ofB1and its infinite graded-symmetric productsym(×B1)∞correspond to the usual higher-spin theory and its multi-particle extension, respectively. The multi-particleB2–higher-spin theory is conjectured to be associated with String Theory.Bp–higher-spin models withp >2 are anticipated to be dual to the rank-pboundary tensor sigma-models.Bphigher- spin models withp≥2 possess two coupling constants responsible for higher-spin interactions inAdSbackground 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 theB2-higher-spin model is shown to demandN≥4 SUSY, suggesting duality with theN= 4 SYM upon spontaneous breaking of higher-spin symmetries. The proposed models are shown to admit unitary truncations. 1