Regularization frames for closed string deformations: String Field Theory vs Polyakov

In this thesis we use Bosonic Open String Field Theory to study tree-level Effective potentials in String Theory. We study a modification of Witten's cubic action by a gauge-invariant closed string deformation (Ellwood invariant). This deformation represents a change in the bulk background and it appears as a tadpole for the open string theory. We then study the effects of canceling the tadpole by an open string shift and we analyze the leading contributions to the resulting effective action. In general, all of them suffer from IR divergences associated to Riemann surface degeneration. We then describe the regularization that is naturally implied by String Field Theory, for both open and closed string degenerations. Subsequently we attempt to understand the SFT regularization from the Polyakov Path Integral perspective. We show that, in all analyzed examples, the results of the SFT regularization are reproduced in the Polyakov approach by the so-called Hadamard regularization, thus providing a method for regularizing these kind of zero-momentum amplitudes directly in a first-quantized setting.