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 canceled 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 noncritical 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.

ACCELERATION OF THE UNIVERSE IN TYPE-0 NONCRITICAL STRINGS

Presently there is preliminary observational evidence that the cosmological constant might be nonzero, and hence that our universe is eternally accelerating (de Sitter). This poses fundamental problems for string theory, since a scattering matrix is not well defined in such universes. In a previous paper we have presented a model, based on (nonequilibrium) noncritical strings, which is characterized by eventual "graceful" exit from a de Sitter phase. The model is based on a type-0 string theory, involving D3 brane worlds, whose initial quantum fluctuations induce the noncriticality. We argue in this paper that this model is compatible with the current observations. A crucial role for the correct "phenomenology" of the model is played by the relative magnitude of the flux of the five-form of the type 0 string to the size of five of the extra dimensions, transverse to the direction of the flux-field. We do not claim, at this stage at least, that this model is a realistic physical model for the universe, but we find it interesting that the model cannot be ruled out immediately, at least on phenomenological grounds.

THE WALL OF THE CAVE

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang–Mills theories must be described by the noncritical strings in the five-dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang–Mills theories. The article is written on the occasion of the 40th anniversary of the IHES.

D Branes from Liouville Strings

We develop quantization aspects of our Liouville approach to noncritical strings, proposing a path-integral formulation of a second quantization of string theory, that incorporates naturally the couplings of string sources to background fields. Such couplings are characteristic of macroscopic string solutions and/or D-brane theories. Resummation over world-sheet genera in the presence of stringy (σ-model) soliton backgrounds, and recoil effects associated with logarithmic operators on the world sheet, play a crucial role in inducing such sources as well-defined renormalization-group counterterms. Using our Liouville renormalization group approach, we derive the appropriate second-order equation of motion for the D brane. We discuss within this approach the appearance of open strings, whose ends carry nontrivial Chan–Paton-like quantum numbers related to the W∞ charges of two-dimensional string black holes.

THE BRST SYMMETRY OF AFFINE LIE SUPERALGEBRAS AND NONCRITICAL STRINGS

The topological field theories associated with affine Lie superalgebras are constructed. Their BRST symmetry is characterized by a Kazama algebra containing spin 1, 2 and 3 operators and closes linearly. Under this symmetry all operators are grouped into BRST doublets. The relation between the models constructed and noncritical string theories is explored.