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.

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We study a topological Landau-Ginzburg model with superpotential W (X) = X −1 . This is argued to be equivalent to c = 1 string theory compactified at the self-dual radius.We compute the tree-level correlation function of N tachyons in this theory and show their agreement with matrix-model results. We also discuss the nature of contact terms, the perturbed superpotential and the flow of operators in the small phase space. The role of gravitational descendants in this theory is examined, and the tachyon two-point function in genus 1 is obtained using a conjectured modification of the gravitational recursion relations.

An appropriate field configuration in non-polynomial closed string field theory is shown to correspond to a general off-shell field configuration in low energy effective field theory. A set of string field theoretic symmetries that act on the fields in low energy effective field theory as general coordinate transformation and antisymmetric tensor gauge transformation is identified. The analysis is carried out to first order in the fields; thus the symmetry transformations in string field theory reproduce the linear and the first non-linear terms in the gauge transformations in the low energy effective field theory. Prefitem

Spacetime properties of the tachyon of the p-adic string theory can be derived from a (non-local) action on the p-adic line Q p , thought of as the boundary of the 'worldsheet'. We show that a term corresponding to the background of the antisymmetric second rank tensor field B can be added to this action. We examine the consequences of this term, in particular, its relation to a noncommutative deformation of the effective theory of the p-adic tachyon in spacetime.