Tachyon condensation and large N transition in topological strings

The thesis consists of the two separate parts. The first part is devoted to the study of tachyon condensation in unstable D-branes using the framework of boundary independent string field theory. The subject of the second part is Chern-Simons matrix models and large N transitions in topological strings.; We calculate the background independent action for bosonic and supersymmetric open string field theory in a constant B-field. We also determine the tachyon effective action in the presence of constant B-field. In addition using boundary string field theory we study the decay of unstable D-branes to lower dimensional D-branes via the tachyon condensation at one loop level. We analyze one loop divergences and use the Fischler-Susskind mechanism to cancel divergences arising at the boundary of moduli space. The tachyon action up to the second derivative is obtained and a logarithmic correction to the tachyon potential is written down explicitly. Multiple D-branes is also considered and the role of the boundary fermions is highlighted.; In the second part we study the saddle point approximation of Chern-Simons matrix models. For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is proportional to the derivative of the genus zero free energy F0. Motivated by the fact that this relationship does not hold for Chern-Simons theory on S 3, we calculate the sub-leading free energy in the matrix model for this theory, which is a Gaussian matrix model with Haar measure on the group SO/Sp. We derive a quantum loop equation for this matrix model and then find that F1 is an integral of the leading order resolvent over the spectral curve. We explicitly calculate this integral for quadratic potential and find agreement with previous studies of SO/Sp Chern-Simons theory. We also demonstrate that the spectral curve of the matrix model for Chern-Simons theory on the Lens space S3/Z p is precisely the Riemann surface which appears in the mirror to the blownup, orbifolded conifold. This provides the first check of the A-model large N duality for T*(S3/Z p), p > 2. We check the large N transition for "local" conifold using the large N limit of the corresponding Chern-Simons two matrix model. We find the spectral curve and calculate the genus zero free energy.