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内容記述 |
We consider bosonic noncritical strings as QCD strings and we present a basic strategy to construct them in the context of Liouville theory. We show that Dirichlet boundary conditions play important roles in generalized Liouville theory. Specifically, they are used to stabilize the classical configuration of strings and also utilized to treat tachyon condensation in our model. <br /><br /> At the beginning of the thesis, we review the relation between gauge theories and string theories, and we make basic presuppositions and assumptions for further discussion to construct QCD strings. Here "QCD strings" mean strings which describe four-dimensional non-SUSY large-N pure Yang-Mills theory, where quarks are not dynamical. We assume that the boundaries of open QCD strings correspond to the Wilson loops in Yang-Mills theory. We consider a noncritical (four-dimensional) bosonic string as a natural candidate for such a QCD string. Noncritical strings, in the spacetime where the dimension is lower than one, can be consistently quantized in the framework of Liouville theory. Therefore, we attempt to generalize it to higher-dimensional cases. Namely, we consider a generalized Liouville theory as such a QCD string, and attempt to quantize it. In this thesis, the generalized Liouville theory is assumed to be the Liouville theory in general backgrounds.<br /> One of the main problems here is the stabilization of the Liouville mode while preserving Weyl invariance. We discuss several ideas for it, and we find that we can stabilize the Liouville mode with Dirichlet boundary conditions. In general, Dirichlet boundary conditions for the Liouville mode break Weyl invariance on the world-sheet, because we have a dilaton which has non-trivial dependence on the Liouville mode. However, we point out that they maintain Weyl invariance, if an appropriate condition is satisfied. We obtain the criterion for consistent Dirichlet boundary conditions at the one-loop level of the non-linear sigma model on the world-sheet. This method has a desirable property; the stabilized value of the Liouville mode is independent on the Euler number of the world-sheet, and we can stabilize it for all the topology of the world-sheet. <br /> We also analyze the perturbative solutions of the equation of motion for the backgrounds. It is shown that we have a suitable solution, at the one-loop level, which satisfies the criterion for Weyl invariance. Furthermore, this argument leads us to the unique selection of the branch of the solutions; although we have several branches of the solutions, we can select the unique branch among them by examining whether it allows consistent Dirichlet boundary conditions or not.<br /> The other problem is the existence of tachyons. We also discuss tachyon condensation. Although complete treatment of it is very difficult, we present a simple strategy for it in the framework of generalized Liouville theory. The idea we present is to attach "tadpoles" to the world-sheet. They have a role to alter the string vacuum. We surmise that the "tadpole" in Liouville theory might be represented as a macroscopic hole on the world-sheet with Dirichlet boundary conditions, where the Dirichlet boundary condition for the Liouville mode is restricted by the criterion for Weyl invariance. Furthermore, the macroscopic hole on the world-sheet should be mapped into a single point in the target space. This is because, they should not be observed in the target space. Therefore, the boundary conditions on the macroscopic hole as a tadpole should be D-instanton-like Dirichlet boundary conditions. Although a similar proposal to alter string vacuum with D-instantons has already given for critical strings, we insist that we can also use the above method for the generalized Liouville theory. The insertion of such D-instanton-like boundaries into the world-sheet does not break our basic presuppositions and assumptions presented in the beginning of the thesis. Furthermore, we guess that the non-perturbative effects in Liouville theory are different from those of critical strings. This is because the moduli space, namely the regions for the target-space coordinates of the D-instanton-like tadpoles which should be integrated over, is different from those for ordinary strings with a constant dilaton. This is because, we have the restriction comes from the criterion for Weyl invariance mentioned above.<br /><br /> To sum up our main statement in this thesis, Dirichlet boundary conditions have an important roles in the generalized Liouville theory, and they can be imposed on the Liouville mode while preserving Weyl invariance if the appropriate condition is satisfied. The investigation of Dirichlet strings in dilatonic backgrounds is very important, and it should yield necessary information about the construction of noncritical strings. |
要旨・審査要旨 / Abstract, Screening Result (260.8 kB)
