arXiv subjects
Publications and source records attributed to Nobuyuki Ishibashi.
We construct the Hamiltonian operator of the string field theory for $c=0$ string theory. It describes how strings evolve in the coordinate frame, which is defined by using the geodesic distance on the worldsheet. The Hamiltonian consists of three-string interaction terms and a tadpole term. We show that one can derive the loop amplitudes of $c=0$ string theory from this Hamiltonian.
We consider self-avoiding Nambu-Goto open strings on a random surface. We have shown that the partition function of such a string theory can be calculated exactly. The string susceptibility for the disk is evaluated to be $-\frac{1}{2}$. We also consider modifications of the Nambu-Goto action which are exactly soluble on a random surface.
It is known that Liouville theory can be represented as an SL(2,R) gauged WZW model. We study a two dimensional field theory which can be obtained by analytically continuing some of the variables in the SL(2,R) gauged WZW model. We can derive Liouville theory from the analytically continued model, ( which is a gauged SL(2,C)/SU(2) model, ) in a similar but more rigorous way than from the original gauged WZW model. We investigate the observables of this gauged SL(2,C)/SU(2) model. We find infinitely many extra observables which can not be identified with operators in Liouville theory. We concentrate on observables which are $(1,1)$ forms and the correlators of their integrals over two dimensional spacetime. At a special value of the coupling constant of our model, the correlators of these integrals on the sphere coincide with the results from matrix models.