Open minimal strings and open Gelfand-Dickey hierarchies

Aleshkin, Konstantin (0000 0001 2299 7671, L.D. Landau Institute for Theoretical Physics, Akademika Semenova av. 1-A, 142432, Chernogolovka, Moscow region, Russia) (0000 0004 1762 9868, International School of Advanced Studies (SISSA), via Bonomea 265, 34136, Trieste, Italy) ; Belavin, Vladimir (0000 0001 0656 6476, I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky ave. 53, 119991, Moscow, Russia) (0000 0004 0619 6198, Department of Quantum Physics, Institute for Information Transmission Problems, Bolshoy Karetny per. 19, 127994, Moscow, Russia) (0000 0004 0604 7563, Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, 7610001, Israel)

10 February 2019

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.

Published in: JHEP 1902 (2019) 043
Published by: Springer/SISSA
DOI: 10.1007/JHEP02(2019)043
arXiv: 1811.04066
License: CC-BY-4.0

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