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Journal of High Energy Physics

, 2019:43 | Cite as

Open minimal strings and open Gelfand-Dickey hierarchies

  • Konstantin AleshkinEmail author
  • Vladimir Belavin
Open Access
Regular Article - Theoretical Physics
First Online:
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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.

Keywords

Conformal Field Models in String Theory Integrable Hierarchies Matrix Models 
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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.L.D. Landau Institute for Theoretical PhysicsChernogolovkaRussia
  2. 2.International School of Advanced Studies (SISSA)TriesteItaly
  3. 3.I.E. Tamm Department of Theoretical PhysicsP.N. Lebedev Physical InstituteMoscowRussia
  4. 4.Department of Quantum PhysicsInstitute for Information Transmission ProblemsMoscowRussia
  5. 5.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael

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