Scaling Self-Similar Formulation of the String Equations of the Hermitian Matrix Model

The string equation appearing in the double scaling limit of the Hermitian one--matrix model, which corresponds to a Galilean self--similar condition for the KdV hierarchy, is reformulated as a scaling self--similar condition for the Ur--KdV hierarchy. A non--scaling limit analysis of the one--matrix model has led to the complexified NLS hierarchy and a string equation. We show that this corresponds to the Galilean self--similarity condition for the AKNS hierarchy and also its equivalence to a scaling self--similar condition for the Heisenberg ferromagnet hierarchy.Comment: 12 pages in AMS-LaTeX, AMS-LaTeXable versio

Extra States and Symmetries in D<2 Closed String Theory

We show that there is (p-1)(p'-1) dimensional semi-relative BRST cohomology at each non-positive ghost number in the (p,p') minimal conformal field theory coupled to two dimensional quantum gravity. These closed string states are related to currents and symmetry charges of `exotic' ghost number. We investigate the symmetry structure generated by the most conventional currents (those of vanishing total ghost number), and make a conjecture about the extended algebra which results from incorporating the currents at negative ghost number.Comment: 15 page

W-Algebra Symmetries of Generalised Drinfel'd-Sokolov Hierarchies

Using the zero-curvature formulation, it is shown that W-algebra transformations are symmetries of corresponding generalised Drinfel'd-Sokolov hierarchies. This result is illustrated with the examples of the KdV and Boussinesque hierarchies, and the hierarchy associated to the Polyakov-Bershadsky W-algebra.Comment: 13 page

Existence of an information unit as a postulate of quantum theory

Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a new set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.Comment: Published version - 6 pages, 3 appendices, 3 figure

Algebraic Structures and Differential Geometry in 2D String Theory

A careful treatment of closed string BRST cohomology shows that there are more discrete states and associated symmetries in $D=2$ string theory than has been recognized hitherto. The full structure, at the $SU(2)$ radius, has a natural description in terms of abelian gauge theory on a certain three dimensional cone $Q$. We describe precisely how symmetry currents are constructed from the discrete states, explaining the role of the ``descent equations.'' In the uncompactified theory, we compute the action of the symmetries on the tachyon field, and isolate the features that lead to nonlinear terms in this action. The resulting symmetry structure is interpreted in terms of a homotopy Lie algebra.Comment: 65pp. (Two figures, not included.

Generalized Abelian S-duality and coset constructions

Electric-magnetic duality and higher dimensional analogues are obtained as symmetries in generalized coset constructions, similar to the axial-vector duality of two dimensional coset models described by Rocek and Verlinde. We also study global aspects of duality between p-forms and (d-p-2)-forms in d-manifolds. In particular, the modular duality anomaly is governed by the Euler character as in four and two dimensions. Duality transformations of Wilson line operator insertions are also considered.Comment: 20 page

Tachyon Condensates and String Theoretic Inflation

Cosmological solutions of the beta function equations for the background fields of the closed bosonic string are investigated at the one-loop level. Following recent work of Kostelecky and Perry, it is assumed that the spatial sections of the space-time are conformally flat. Working in the sigma-model frame, the non-trivial tachyon potential is utilized to determine solutions with sufficient inflation to solve the smoothness and flatness problems. The graceful exit and density perturbation constraints can also be successfully implemented.Comment: FERMI-PUB 93/074-T, harvmac, 16 page

Extended Inflation from Strings

We study the possibility of extended inflation in the effective theory of gravity from strings compactified to four dimensions and find that it strongly depends on the mechanism of supersymmetry breaking. We consider a general class of string--inspired models which are good candidates for successful extended inflation. In particular, the $\omega$--problem of ordinary extended inflation is automatically solved by the production of only very small bubbles until the end of inflation. We find that the inflaton field could belong either to the untwisted or to the twisted massless sectors of the string spectrum, depending on the supersymmetry breaking superpotential.Comment: 18p