Mysterious zero in AdS5xS5 supergravity -: art. no. 105023

It is shown that all the states in AdS(5)xS(5) supergravity have zero eigenvalue for all Casimir eigenvalues of its symmetry group SU(2,2\4). To compute this zero in supergravity we refine the oscillator methods for studying the lowest weight unitary representations of SU(N,M\R+S). We solve the reduction problem when one multiplies an arbitrary number of super-doubletons. This enters in the computation of the Casimir eigenvalues of the lowest weight representations. We apply the results to SU(2,2\4) that classifies the Kaluza-Klein towers of ten-dimensional type IIB supergravity compactified on AdS(5)xS(5). We show that the vanishing of the SU(2,2\4) Casimir eigenvalues for all the states is indeed a group-theoretical fact in AdS(5)xS(5) supergravity. By the AdS-CFT correspondence, it is also a fact for gauge invariant states of super-Yang-Mills theory with four supersymmetries in four dimensions. This nontrivial and mysterious zero is very interesting because it is predicted as a straightforward consequence of the fundamental local Sp(2) symmetry in 2T-physics. Via the 2T-physics explanation of this zero we find a global indication that these special supergravity and super-Yang-Mills theories hide a twelve-dimensional structure with (10,2) signature.