Abstract
We study the interactions of Maldacena's long folded strings in two-dimensional string theory. We find the amplitude for a state containing two long folded strings to come and go back to infinity. We calculate this amplitude both in the worldsheet theory and in the dual matrix model, the matrix quantum mechanics. The matrix model description allows to evaluate the amplitudes involving any number of long strings, which are given by the mixed trace correlators in an effective two-matrix model.
Highlights
In this paper we study the scattering of long folded strings in 2D string theory
In this paper we studied the simplest scattering processes of long folded strings in the twodimensional string theory
We used the description of the long strings in terms of a FZZT brane with μB ≫ √μ, as suggested in [1]
Summary
In this paper we study the scattering of long folded strings in 2D string theory. As pointed out by Maldacena [1], long folded strings stretching from infinity correspond to non-singlet states in the dual matrix model. When the ends of the string reach φ ∼ − log μB, they get trapped by the brane, while the bulk of the string continues to move until it looses all its kinetic energy at distance φ ∼ − log μ and starts to evolve back This picture allows to express the reflection amplitude for the tip of a long folded string as a certain limit of the boundary two-point function in Liouville theory. Using the chiral formalism, the scattering problem in the non-singlet sector of MQM was reformulated by one of the authors [18] in terms of the mixed trace correlators in an effective two-matrix model This allowed to apply some powerful results derived for the two-matrix model [19, 20]. We argue that such an amplitude again decomposes into elementary processes, reflections of long strings and scattering of any number k ≤ n of short open strings
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