New Superstring Isometries and Hidden Dimensions

Dimitri Polyakov

Published 2007-06-02, updated 2007-06-05Version 2

We explore 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 $\alpha$-symmetries, are induced by special space-time generators, violating the equivalence of ghost pictures. We classify the $\alpha$-symmetry generators in terms of superconformal ghost cohomologies $H_{n}\sim{H_{-n-2}}(n\geq{0})$ and associate these generators with a chain of hidden space-time dimensions, with each ghost cohomology $H_{n}\sim{H_{-n-2}}$ ``contributing'' an extra dimension. Namely, we show that each ghost cohomology $H_{n}\sim{H_{-n-2}}$ of non-critical superstring theory in $d$-dimensions contains $d+n+1$ $\alpha$-symmetry generators and the generators from $H_{k}\sim{H_{-k-2}},1\leq{k}\leq{n}$, 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 $\alpha$-generators are identified with the extra symmetries of the $2T$-physics formalism, also known to originate from a hidden space-time dimension.