Loop equations and KDV hierarchy in 2-D quantum gravity

Journal Article · Mon Apr 20 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92001022· OSTI ID:5196267

Fucito, F ^[1]; Martellini, M ^[2]

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1. CERN, 1211 Geneva 23 (CH)
2. Theoretical Physics, ETH-Hoenggerberg, 8093 Zurich (CH)

In this paper a derivation of the loop equation for two-dimensional quantum gravity from the KdV equations and the string equation of the one-matrix model is given. The loop equation was found to be equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the virasoro algebra. Starting form the equations expressing these constraints. The authors are able to rederive the equations of the KdV hierarchy using the vertex operator construction of the A{sup (I)}{sub I} infinite dimensional twisted Kac-Moody algebra. From these considerations it follows that the solutions of the string equation of the one-matrix model are given by a subset of the solutions of the KdV hierarchy.

• OSTI ID: 5196267
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:10; ISSN IMPAE; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
661310 -- Relativity & Gravitation-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
EXTENDED PARTICLE MODEL
FIELD THEORIES
FUNCTIONS
KORTEWEG-DE VRIES EQUATION
MATHEMATICAL MODELS
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PARTITION FUNCTIONS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUARK MODEL
STRING MODELS
SYMMETRY GROUPS
TWO-DIMENSIONAL CALCULATIONS
WILSON LOOP