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Register a new userAnalytic Study of Nonperturbative Solutions in Open String Field Theory
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We propose an analytic framework to study the nonperturbative solutions of Wittens open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution.
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We construct rolling tachyon solutions of open and boundary string field theory (OSFT and BSFT, respectively), in the bosonic and supersymmetric (susy) case. The wildly oscillating solution of susy OSFT is recovered, together with a family of time-dependent BSFT solutions for the bosonic and susy string. These are parametrized by an arbitrary constant r involved in solving the Green equation of the target fields. When r=0 we recover previous results in BSFT, whereas for r attaining the value predicted by OSFT it is shown that the bosonic OSFT solution is the derivative of the boundary one; in the supersymmetric case the relation between the two solutions is more complicated. This technical correspondence sheds some light on the nature of wild oscillations, which appear in both theories whenever r>0.
We study covariant open bosonic string field theories on multiple $Dp$-branes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple $Dp$-branes, we obtain the field theoretical effective action in the zero-slope limit. On the multiple $D0$-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between the open string field theory on multiple $D$-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) matrix model. The covariant open string field theory on multiple $Dp$-branes would be useful to study the non-perturbative properties of quantum field theories in $(p+1)$-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using the covariant string field theory.
Using string scattering amplitudes of open bosonic string on a single $D$-brane, we construct a local field theoretical action for tachyon fields. Cubic local interactions between various particles, belonging to the particle spectrum of string may be directly followed from three-string scattering amplitude. These cubic local interactions may generate perturbative non-local four-particle interactions, which may contribute to four-string scattering amplitude. It was observed that tachyon field in open bosonic string theory must be represented by a complex field in order to reproduce the Veneziano amplitude, describing four-tachyon scattering. The Veneziano amplitude, expanded in terms of $s$-channel poles was compared with the four-tachyon scattering amplitudes in $s$-channel generated perturbatively and it was found that a quartic potential term is needed in the local field theoretical action, which describes open string theory effectively in the low energy regime. With this quartic term, the tachyon potential has a stable minimum point and the tachyon field may condensate. As a result, both tachyon and gauge fields become massive at Planck scale and completely disappear from the low energy particle spectrum.
Simple analytic solution to cubic Neveu-Schwarz String Field Theory including the $GSO(-)$ sector is presented. This solution is an analog of the Erler-Schnabl solution for bosonic case and one of the authors solution for the pure $GSO(+)$ case. Gauge transformations of the new solution to others known solutions for the $NS$ string tachyon condensation are constructed explicitly. This gauge equivalence manifestly supports the early observed fact that these solutions have the same value of the action density.
We study a matrix version of the purely cubic open string field theory as describing the expansion around the closed string vacuum. Any D-branes in the given closed string background can appear as classical solutions by using the identity projectors. Expansion around this solution gives the correct kinetic term for the open strings on the created D-branes while there are some subtleties in the unwanted degree of freedom.
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