In chapter 1, we give a brief review of SFT, focusing on OSFT and the construction of VSFT. We also give some outline about the recently found solution to the OSFT equation of motion. Chapter 2 deals with the construction of time-dependent solutions in VSFT. We start by reviewing how to construct static classical solutions and then we turn to the time-dependent ones. We construct these solutions both in a trivial and in a E-field background. We show that these solutions really interpolate between the two vacua and we point out some points of resemblance between our solution and Sen 's rolling tachyon solution. In the case of an E-field background, after the decay we find a flat profile in the transverse direction to the brane and this ought to be interpreted as fundamental strings, which are polarized by the eletric field and thereby hampered from decaying. We conclude the chapter by presenting some solutions in VSFT that are supposed to describe these fundamental strings. In chapter 3, we exit from the main subject of this thesis and we show some results concerning integrability properties in Light-Cone Open String Field Theory. We show that the three strings vertex coefficients in light-cone open string field theory satisfy the Hirota equations for the dispersionless Toda lattice hierarchy. We also show that Hirota equations allow us to calculate the correlators of an associated quantum system where the Neumann coefficients represent the two-point functions. We consider next the three strings vertex coefficients of the light-cone string field theory on a maximally supersymmetric pp-wave background. Using the previous results we are able to show that these Neumann coefficients satisfy the Hirota equations for the full Toda lattice hierarchy at least up to second order in the string massμ. In chapter 4, we show that a family of 1/2-BPS states of N = 4 SYM is in correspondence with a family of classical solutions of VSFT with a B-field playing the role of the inverse Planck constant. We establish this correspondence by relating the Wigner distributions of the N fermion systems representing such states to low energy space profiles of systems of VSFT D-branes. In this context the Pauli exclusion principle appears as a consequence of the VSFT projector equation. The family of 1/2-BPS states maps through coarse-graining to droplet LLM supergravity solutions. We also discuss the possible meaning of the corresponding coarse graining in the VSFT side. Clearly, one should go into the realm of Superstring Field Theory in order to describe nature. Hence, in chapter 5, we make a brief review about Superstring Field Theory, describing some attempts to construct it and their respective failures. Firstly, we describe Witten's formulation that is an extension of the bosonic theory with insertions of picture changing operators, which introduce divergences in the theory already at the classical level. Moreover, the tachyon potential computed within this framework does not possess a minimum, contradicting Sen's conjectures. Secondly, we present an improved version of Witten's theory that uses a two-step picture changing operator, thereby solving the two forementioned problems. However, it presents other drawbacks like the possibility of different theories off-shell and non-physical states being also a solution to the equation of motion. We finish with chapter 6, where we present some conclusions and open problems. In the appendices, we give some technical details needed in the analysis we make within the body of the thesis.
|Autori:||Scherer Santos, Ricardo Jose|
|Titolo:||String Field Theory: Time-Dependent Solutions and Other Aspects|
|Data di pubblicazione:||26-set-2006|
|Appare nelle tipologie:||8.1 PhD thesis|