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 massĪ¼.
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.
