String field theory, non-commutativity and higher spins

In Chapter 1, we give an introduction to the topic of open string field theory. The concepts presented include gauge invariance, tachyon condensation, as well as the star product.In Chapter 2, we give a brief review of vacuum string field theory (VSFT), an approach to open string field theory around the stable vacuum of the tachyon. We discuss the sliver state explaining its role as projector in the space of half-string basis. We review the construction of D-brane solutions in vacuum string field theory. We show that in the sliver basis the star product correspond to a matrix product. Using the material introduced in the previous chapters, in Chapter 3 we establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, we show that (off--shell) level--matched closed string states are represented by star algebra projectors in open string field theory. As an outcome of our identification, we show that boundary states, which in closed string theory represent D-branes, correspond to the identity string field in the open string side. We then turn to noncommutative field theories. In Chapter 4, we introduce the framework in which we will work. The tools introduced are solitons, projectors, and partial isometries.The ideas of Chapter 4 are applied to specific examples in Chapter 5, where we present new solutions of noncommutative gauge theories in which coincident vortices expand into circular shells. As the theories are noncommutative, the naive definition of the locations of the vortices and shells is gauge-dependent, and so we define and calculate the profiles of these solutions using the gauge-invariant noncommutative Wilson lines introduced by Gross and Nekrasov. We find that charge 2 vortex solutions are characterized by two positions and a single nonnegative real number, which we demonstrate is the radius of the shell. We find that the radius is identically zero in all 2-dimensional solutions. If one considers solutions that depend on an additional commutative direction, then there are time-dependent solutions in which the radius oscillates, resembling a braneworld description of a cyclic universe. There are also smooth BIon-like space-dependent solutions in which the shell expands to infinity, describing a vortex ending on a domain wall.In Chapter 6, we review the Fronsdal models for free high-spin fields that exhibit peculiar properties. We discuss the triplet structure of totally symmetric tensors of the free String Field Theory and their generalization to AdS background.In Chapter 7, in the context of massless higher spin gauge fields in constant curvature spaces discussed in chapter 6, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and the angular momentum for asymptotically flat gravitational fields. We show that there is a one-to-one map from surface charges onto divergence free Killing tensors. These Killing tensors are computed by relating them to a cohomology group of the first quantized BRST model underlying the Fronsdal action.Doctorat en Sciences