New Superstring Isometries and Hidden Dimensions

We study the hierarchy of hidden space-time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is cancelled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space-time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies Hn ∼ H−n−2(n ≥ 0) and associate these generators with a chain of hidden space-time dimensions, with each ghost cohomology Hn ∼ H−n−2 “contributing” an extra dimension. Namely, we show that each ghost cohomology Hn ∼ H−n−2 of non-critical superstring theory in d-dimensions contains d+ n+ 1 α-symmetry generators and the generators from Hk ∼ H−k−2, 1 ≤ k ≤ n, combined together, extend the space-time isometry group from the naive SO(d, 2) to SO(d + n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T -physics formalism, also known to originate from a hidden space-time dimension. PACS:04.50.+ h;11.25.Mj. June 2007 † [email protected]