Open minimal strings and open Gelfand-Dickey hierarchies

• Main Authors: Konstantin Aleshkin, Vladimir Belavin
• Format: Article
• Language: English
• Published: SpringerOpen 2019-02-01
• Series: Journal of High Energy Physics
• Subjects: Conformal Field Models in String Theory; Integrable Hierarchies; Matrix Models
• Online Access: http://link.springer.com/article/10.1007/JHEP02(2019)043

Abstract We study the connection between minimal Liouville string theory and generalized open KdV hierarchies. We are interested in generalizing Douglas string equation formalism to the open topology case. We show that combining the results of the closed topology, based on the Frobenius manifold structure and resonance transformations, with the appropriate open case modification, which requires the insertion of macroscopic loop operators, we reproduce the well-known result for the expectation value of a bulk operator for the FZZT brane coupled to the general (q, p) minimal model. The matching of the results of the two setups gives new evidence of the connection between minimal Liouville gravity and the theory of Topological Gravity.