Hidden 12-dimensional structures in AdS(5)xS(5) and M(4)xR(6)   Supergravities
  It is shown that AdS(5)xS(5) supergravity has hitherto unnoticed supersymmetric properties that are related to a hidden 12-dimensional structure. The totality of the AdS(5)xS(5) supergravity Kaluza-Klein towers is given by a single superfield that describes the quantum states of a 12-dimensional supersymmetric particle. The particle has super phase space (X,P,Theta) with (10,2) signature and 32 fermions. The worldline action is constructed as a generalization of the supersymmetric particle action in Two-Time Physics. SU(2,2|4) is a linearly realized global supersymmetry of the 2T action. The action is invariant under the gauge symmetries Sp(2,R), SO(4,2),SO(6), and fermionic kappa. These gauge symmetries insure unitarity and causality while allowing the reduction of the 12-dimensional super phase space to the correct super phase space for AdS(5)xS(5) or M(4)xR(6) with 16 fermions and one time, or other dually related one time spaces. One of the predictions of this formulation is that all of the SU(2,2|4) representations that describe Kaluza-Klein towers in AdS(5)xS(5) or M(4)xR(6) supergravity universally have vanishing eigenvalues for all the Casimir operators. This prediction has been verified directly in AdS(5)xS(5) supergravity. This suggests that the supergravity spectrum supports a hidden (10,2) structure. A possible duality between AdS(5)xS(5) and M(4)xR(6) supergravities is also indicated. Generalizations of the approach applicable 10-dimensional super Yang Mills theory and 11-dimensional M-theory are briefly discussed. 
Itzhak Bars