One of the most interesting problems in string theory is to understand how the background spacetime on which the string propagates arises in a selfconsistent way. For open strings, there are two main approaches to this problem, boundary string field theory (BSFT) and cubic string field theory (CSFT). In the first part of this Thesis we deal with the construction of the spacetime tachyon effective action in BSFT. Renormalization fixed points are solutions of classical equations of motion and should be viewed as solutions of classical string field theory. We have constructed the WittenShatashvili (WS) spacetime action S and shown that some solitonic solutions are lower dimensional Dbranes for which the finite value of S provides a quite accurate prediction of the Dbrane tension. We have derived the explicit relation between the CSFT and WS action as a field redefinition which is nonsingular onshell only when the normalization factor in the WS action coincides with the tension of the D25brane, in agreement with the conjectures involving tachyon condensation. We have also found a timedependent solution of CSFT whose evolution is driven by a diffusion equation that makes the equations of motion local with respect to the time variable. The analysis here proposed has attracted a good deal of attention for its potential cosmological applications. The profile can be expressed in terms of a series in powers of exponentials of the time coordinate, and gives evidence of a welldefined but wildly oscillatory behavior. The tachyon rolls well past the minimum of the potential, then turns around and begins to oscillate with ever increasing amplitude. Furthermore, we have derived an analytic series solution of the elliptic equations providing the 4tachyon offshell amplitude. From such a solution we computed the exact coefficient of the quartic effective action relevant for timedependent solutions and we derived the exact coefficient of the quartic tachyon coupling. We studied the rolling tachyon solution expressed as a series of exponentials of the time coordinate both using leveltruncation computations and the exact 4tachyon amplitude. The results for the leveltruncated coefficients converge to those derived using the exact string amplitude and confirm the wild oscillatory behavior. In the second part of the Thesis we consider the extension of the gauge/gravity correspondence to systems with reduced and hence more realistic supersymmetry, which is one of the main steps towards a nonperturbative description of confining, QCDlike, gauge theories in terms of gravitational backgrounds. If string theory on AdS5xS5 is integrable, the theory on simple orbifolds of that space would also be expected to be integrable. We have computed the planar finite size corrections to the spectrum of the dilatation operator acting on states of a certain limit of conformal N = 2 quiver gauge field theory which is a ZMorbifold of N = 4 SYM theory. We matched the result to the string dual, IIB superstrings on a ppwave background with a periodically identified null coordinate. Up to two loops, we have shown that the computations done by using an effective Hamiltonian technique and a twisted Bethe Ansatz agree with each other and also agree with a computation of the analogous quantity in string theory. Our results are consistent with integrability of the N = 2 theory.
Non trivial string backgrounds: Tachyons in String Field Theory and Planewaves in DLCQ Strings / Forini, Valentina.  (2006), pp. 1120.
Non trivial string backgrounds: Tachyons in String Field Theory and Planewaves in DLCQ Strings
Forini, Valentina
20060101
Abstract
One of the most interesting problems in string theory is to understand how the background spacetime on which the string propagates arises in a selfconsistent way. For open strings, there are two main approaches to this problem, boundary string field theory (BSFT) and cubic string field theory (CSFT). In the first part of this Thesis we deal with the construction of the spacetime tachyon effective action in BSFT. Renormalization fixed points are solutions of classical equations of motion and should be viewed as solutions of classical string field theory. We have constructed the WittenShatashvili (WS) spacetime action S and shown that some solitonic solutions are lower dimensional Dbranes for which the finite value of S provides a quite accurate prediction of the Dbrane tension. We have derived the explicit relation between the CSFT and WS action as a field redefinition which is nonsingular onshell only when the normalization factor in the WS action coincides with the tension of the D25brane, in agreement with the conjectures involving tachyon condensation. We have also found a timedependent solution of CSFT whose evolution is driven by a diffusion equation that makes the equations of motion local with respect to the time variable. The analysis here proposed has attracted a good deal of attention for its potential cosmological applications. The profile can be expressed in terms of a series in powers of exponentials of the time coordinate, and gives evidence of a welldefined but wildly oscillatory behavior. The tachyon rolls well past the minimum of the potential, then turns around and begins to oscillate with ever increasing amplitude. Furthermore, we have derived an analytic series solution of the elliptic equations providing the 4tachyon offshell amplitude. From such a solution we computed the exact coefficient of the quartic effective action relevant for timedependent solutions and we derived the exact coefficient of the quartic tachyon coupling. We studied the rolling tachyon solution expressed as a series of exponentials of the time coordinate both using leveltruncation computations and the exact 4tachyon amplitude. The results for the leveltruncated coefficients converge to those derived using the exact string amplitude and confirm the wild oscillatory behavior. In the second part of the Thesis we consider the extension of the gauge/gravity correspondence to systems with reduced and hence more realistic supersymmetry, which is one of the main steps towards a nonperturbative description of confining, QCDlike, gauge theories in terms of gravitational backgrounds. If string theory on AdS5xS5 is integrable, the theory on simple orbifolds of that space would also be expected to be integrable. We have computed the planar finite size corrections to the spectrum of the dilatation operator acting on states of a certain limit of conformal N = 2 quiver gauge field theory which is a ZMorbifold of N = 4 SYM theory. We matched the result to the string dual, IIB superstrings on a ppwave background with a periodically identified null coordinate. Up to two loops, we have shown that the computations done by using an effective Hamiltonian technique and a twisted Bethe Ansatz agree with each other and also agree with a computation of the analogous quantity in string theory. Our results are consistent with integrability of the N = 2 theory.File  Dimensione  Formato  

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