Emergent Spacetime

We summarize the arguments that space and time are likely to be emergent notions; i.e. they are not present in the fundamental formulation of the theory, but appear as approximate macroscopic concepts. Along the way we briefly review certain topics. These include ambiguities in the geometry and the topology of space which arise from dualities, questions associated with locality, various known examples of emergent space, and the puzzles and the prospects of emergent time.Comment: Rapporteur talk at the 23rd Solvay Conference in Physics, December, 2005. 24 page

Observations On The Moduli Space Of Two Dimensional String Theory

We explore the moduli space of the two dimensional fermionic string with linear dilaton. In addition to the known 0A and 0B theories, there are two theories with chiral GSO projections, which we call IIA and IIB. They are similar to the IIA and IIB theories of ten dimensions, but are constructed with a different GSO projection. Compactifying these theories on various twisted circles leads to eight lines of theories. Three of them, 0A on a circle, super-affine 0A and super-affine 0B are known. The other five lines of theories are new. At special points on two of them we find the noncritical superstring.Comment: 19 pages, one figure, minor change

Flux Vacua and Branes of the Minimal Superstring

We analyze exactly the simplest minimal superstring theory, using its dual matrix model. Its target space is one dimensional (the Liouville direction), and the background fields include a linear dilaton, a possible tachyon condensate, and RR flux. The theory has both charged and neutral branes, and these exhibit new and surprising phenomena. The smooth moduli space of charged branes has different weakly coupled boundaries in which the branes have different RR charges. This new duality between branes of different charges shows that the semiclassical notion of localized charge is not precise in the quantum theory, and that the charges of these branes can fluctuate. Correspondingly, the RR flux in some parts of target space can also fluctuate -- only the net flux at infinity is fixed. We substantiate our physical picture with a detailed semiclassical analysis of the exact answers. Along the way, we uncover new subtleties in super-Liouville theory.Comment: 46 pages, 3 figures, new identities for the neutral brane, references added, minor change

Minimal String Theory

We summarize recent progress in the understanding of minimal string theory, focusing on the worldsheet description of physical operators and D-branes. We review how a geometric interpretation of minimal string theory emerges naturally from the study of the D-branes. This simple geometric picture ties together many otherwise unrelated features of minimal string theory, and it leads directly to a worldsheet derivation of the dual matrix model.Comment: 10 pages, 4 figures, talk presented by NS at Strings '0