String theory and classical integrable systems

Abstract

We discuss different formulations and approaches to string theory and $2d$ quantum gravity. The generic idea to get a unique description of {\it many} different string vacua altogether is demonstrated on the examples in $2d$ conformal, topological and matrix formulations. The last one naturally brings us to the appearance of classical integrable systems in string theory. Physical meaning of the appearing structures is discussed and some attempts to find directions of possible generalizations to ``higher-dimensional" models are made. We also speculate on the possible appearence of quantum integrable structures in string theory.

lecture given at III Baltic Rim student seminar, Helsinki, September 1993} 33pp, latex

References in corpus (15)

• Closed String Field Theory: Quantum Action and the BV Master Equation
• Introduction to string field theory
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Quantum Background Independence In String Theory
• Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
• Towards unified theory of $2d$ gravity
• Generalized Kazakov-Migdal-Kontsevich Model: group theory aspects
• On Equivalence of Topological and Quantum 2d Gravity
• Gravity-Matter Couplings from Liouville Theory
• On Connection between Topological Landau-Ginzburg Gravity and Integrable Systems
• On Exact Evaluation of Path Integrals
• The Many Faces of the Quantum Liouville Exponentials
• Ward identities and W-constraints in Generalized Kontsevich Model
• The operator algebra of the discrete state operators in 2D gravity with non-vanishing cosmological constant
• Mirror Transform and String Theory

Cited by in corpus (1)

• Integrable hierarchies, Hurwitz numbers and a branch point field in critical topologically massive gravity