Aspects of noncommutativity in Field and String theory and Closed String Tachyon Condensation

Abstract

This thesis studies two problems; The first part of the thesis analyses some of the aspects of noncommutativity in field and string theory; The mixing of the ultraviolet and the infrared sectors in noncommutative field theories and their interpretation in terms of open-closed string duality in string theory. And Localised closed string tachyon condensation is analysed in the second part. It is shown that the renormalisation conditions set at a particular momentum configuration with a fixed number of zero momenta, renormalises the Green's functions for any general momenta only when this configuration has same set of zero momenta. In the context of spontaneous symmetry breaking in noncommutative scalar theory, it is shown that the broken phase of the theory the Ward identities are satisfied to all orders only when one keeps an infrared regulator by shifting to a nonconstant vacuum. In the second part the condensation of closed string Tachyons is analysed on the C/ZN orbifold. The potential for the tachyons is constructed upto the quartic interaction term in the large N limit, where there exist near marginal tachyons. The quartic coupling for these tachyons is calculated by subtracting from the string theory amplitude for the tachyons, the contributions from the massless exchanges, computed from the effective field theory.