On the SL(2,Z) Covariant World-Sheet Action with Sources

We analyse various world-sheet properties of the $SL(2,Z)$ covariant type IIB string action by coupling it with $SL(2,Z)$ covariant source.Comment: 8 pages, harvmac, minor changes, journal versio

Holography and Stiff-matter on the Brane

Recently, Verlinde noted a surprising similarity between Friedmann equation governing radiation dominated universe and Cardy's entropy formula in conformal field theory. In this note, we study a brane-universe filled with radiation and stiff-matter. We analyze Friedmann equation in this context and compare our results with Cardy's entropy formula.Comment: 6 pages, Latex, references added to match with published versio

Boundary Fluctuations of AdS String

We analyse the world-sheet perturbations of string theory formulated around $AdS_3$ background. We identify a set of operators that, while added to the world-sheet action, generate the boundary fluctuations of $AdS_3$. The effect of these operators can be collectively defined in terms of Liouville field living on the $AdS_3$ boundary. We then study various deformations of $AdS_3$ generated by boundary fluctuations by turning on suitable world-sheet couplings. We also discuss certain small fluctuations around the BTZ black hole.Comment: 10 pages, harvmac, no figur