Unified non-metric (1, 0) tensor-Einstein supergravity theories and (4, 0) supergravity in six dimensions

The ultrashort unitary (4,0) supermultiplet of 6d superconformal algebra OSp(8*|8) reduces to the CPT-self conjugate 4d SU(2,2|8) that represents fields maximal N=8 supergravity. graviton in multiplet is described by a mixed tensor gauge field which can not be identified with standard metric 6d. Furthermore obtained as double copy (2,0) conformal whose interacting theories are non-Lagrangian. It had been suggested an non-metric supergravity theory might describe strongly coupled phase 5d In this paper we study implications existence truncated (1,0) 5,8 and 14 self-dual multiplets reduce three unified magical d=5. This implies infinite families N=2 , Maxwell-Einstein (MESGTs) plus two sporadic ones must have uplifts Einstein d=6. These non-compact global symmetry groups under all including gravitensor transform irreducibly. Four these scalar manifolds symmetric spaces. other homogeneous We also discuss exceptional theoretic formulations $(1,0)$ tensor-Einstein conclude speculations concerning higher dimensional $(4,0)$ $d=6$.