New Superstring Isometries and Hidden Dimensions

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.Comment: 26 pages typos correcte

String Theory and Emergent AdS Geometry in Higher Spin Field Theories

We analyze the Weyl invariance constraints on higher spin vertex operators in open superstring theory describing massless higher spin gauge field excitations in d-dimensional space-time. We show that these constraints lead to low-energy equations of motion for higher spin fields in AdS space, with the leading order beta-function for the higher spin fields producing Fronsdal's operator in $AdS_{d+1}$, despite that the higher spin vertex operators are originally defined in flat background. The correspondence between the $\beta$-function in string theory and $AdS_{d+1}$ Fronsdal operators in space-time is found to be exact for $d=4$, while for other space-time dimensions it requires modifications of manifest expressions for the higher spin vertex operators. We argue that the correspondence considered in this paper is the leading order of more general isomorphism between Vasiliev's equations and equations of motion of extended open string field theory (OSFT), generalized to include the higher spin operators.Comment: 28 page