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 timedependent solutions in VSFT. We start by reviewing how to construct static classical solutions and then we turn to the timedependent ones. We construct these solutions both in a trivial and in a Efield 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 Efield 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 LightCone Open String Field Theory. We show that the three strings vertex coefficients in lightcone 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 twopoint functions. We consider next the three strings vertex coefficients of the lightcone string field theory on a maximally supersymmetric ppwave 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 1/2BPS states of N = 4 SYM is in correspondence with a family of classical solutions of VSFT with a Bfield 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 Dbranes. In this context the Pauli exclusion principle appears as a consequence of the VSFT projector equation. The family of 1/2BPS states maps through coarsegraining 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 twostep picture changing operator, thereby solving the two forementioned problems. However, it presents other drawbacks like the possibility of different theories offshell and nonphysical 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.
String Field Theory: TimeDependent Solutions and Other Aspects(2006 Sep 26).
String Field Theory: TimeDependent Solutions and Other Aspects

20060926
Abstract
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 timedependent solutions in VSFT. We start by reviewing how to construct static classical solutions and then we turn to the timedependent ones. We construct these solutions both in a trivial and in a Efield 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 Efield 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 LightCone Open String Field Theory. We show that the three strings vertex coefficients in lightcone 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 twopoint functions. We consider next the three strings vertex coefficients of the lightcone string field theory on a maximally supersymmetric ppwave 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 1/2BPS states of N = 4 SYM is in correspondence with a family of classical solutions of VSFT with a Bfield 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 Dbranes. In this context the Pauli exclusion principle appears as a consequence of the VSFT projector equation. The family of 1/2BPS states maps through coarsegraining 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 twostep picture changing operator, thereby solving the two forementioned problems. However, it presents other drawbacks like the possibility of different theories offshell and nonphysical 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.File  Dimensione  Formato  

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