We show that the non-critical c = 1 string at the self-dual radius is equivalent to topological strings based on the deformation of the conifold singularity of Calabi-Yau threefolds. The Penner sum giving the genus expansion of the free energy of the c = 1 string theory at the self-dual radius therefore gives the universal behaviour of the topological partition function of a Calabi-Yau threefold near a conifold point.

We study stringy fluctuations as a source for corrections to the Wilson loop as obtained from the superstring on adS 5 × S 5 /N = 4 SYM correspondence. We give a formal expression in terms of determinants of two-dimensional operators for the leading order correction. 02/99

It has been conjectured that an extremum of the tachyon potential of a bosonic Dbrane represents the vacuum without any D-brane, and that various tachyonic lump solutions represent D-branes of lower dimension. We show that the tree level effective action of p-adic string theory, the expression for which is known exactly, provides an explicit realisation of these conjectures.

We analyse of the effective action of the tachyon field on a D-brane, of both bosonic as well as superstring theory. We find that the non-standard kinetic term of the tachyon field requires a correction to the Born-Infeld type Lagrangian. The cosmological significance of the resulting dynamics is explored.We also examine if the rolling tachyon can provide an effective cosmological constant and contrast its behaviour with quintessence.