Fractional space-like branes

We discuss construction and applications of instanton-like objects which we call fractional space-like branes. These objects are localised at a fixed point of a time-like (or more generally space-time) orbifold which is a string theoretical toy model of a cosmological singularity. We formulate them in boundary state, adsorption, and fermionisation approaches. 1 Fractional space-like branes in a time-like orbifold As a leading candidate of the ultimate theory of high energy physics, string/Mtheory is expected to give physical explanations to highly conceptual issues such as the origin of the Universe. Indeed, in the past decade, much effort has been devoted to constructing consistent cosmological models from a string theory perspective. Various prototypical models, including Pre-BigBang [1], Ekpyrotic [2], and Cyclic [3] scenarios, have emerged and attracted much attention. Although it would be fair to say that these models are rather immature, it is certainly worthwhile, and perhaps rewarding, to investigate string-based cosmological scenarios that could develop string theory into an experiment-backed science. These string-inspired cosmological scenarios typically possess big crunch / big bang singularities. In these scenarios it is customary to assume that, through some resolution mechanism, the Universe undergoes a smooth transition from a big crunch to a big bang so that the history of the universe continues from the infinite past, evolving with bouncing event(s). This certainly poses various challenges. Besides the obvious problem of resolving the singularity, one often needs to implement extremely fine-tuned initial (asymptotic) conditions. Since the age of such a universe is infinite, the second law of thermodynamics is likely to indicate an infinite amount of entropy today (i.e. a dead universe); in order to build a sensible scenario one needs to devise a mechanism to dump or dilute entropy. If we compare these scenarios of string cosmology with the good old standard (big bang + inflationary) cosmology, the unbounded past of the stringinspired models appears to be rather peculiar. It is certainly not that the string