Hidden symmetries, AdS(D)xS(n), and the lifting of one-time physics to two-time physics - art. no. 045019

The massive non-relativistic foe particle in d-1 space dimensions, with a L agrangian L=(m/2)(r) over dot(2), has an action with a surprising non-linea rly realized SO(d,2) symmetry. This is the simplest example of a host of di verse one-time-physics systems with hidden SO(d,2) symmetric actions. By th e addition of gauge degrees of freedom, they can all be lifted to the same SO(d,2) covariant unified theory that includes an extra spacelike and an ex tra timelike dimension. The resulting action in d+2 dimensions has manifest SO(d,2) Lorentz symmetry and a gauge symmetry Sp(2,R). The symmetric actio n defines two-time physics. Conversely, the two-time action can be gauge fi xed to diverse one-time physical systems. In this paper three new gauge fix ed forms that correspond to the non-relativistic particle, the massive rela tivistic particle, and the particle in AdS(d-n)XS(n) curved spacetime will be discussed at the classical level. The last case is discussed at the firs t quantized and field theory levels as well. For the last case the popularl y known symmetry is SO(d-n - 1,2) X SO(n + 1), but yet we show that the cla ssical or quantum versions are symmetric under the larger SO(d,2). in the f ield theory version the action is symmetric under the full SO(d,2) provided it is improved with a quantized mass term that arises as an anomaly from o perator ordering ambiguities. The anomalous mass term vanishes for AdS(2) X S-o and AdS(n) x S-n (i.e., d = 2n). A quantum test for the presence of tw o-time-physics in a one-time physics system is that the SO(d,2) Casimir ope rators have fixed eigenvalues independent of the system. It is shown that t his test is successful for the particle in AdS(d-n) X S-n by computing the Casimir operators and showing explicitly that they are independent of it. T he strikingly larger symmetry could be significant in the context of the pr oposed AdS/CFT duality. [S0556-2821(99)02104-9].