The string difference equation of the D = 1 matrix model and W[sub 1+[infinity]] symmetry of the KP hierarchy

Journal Article · Mon Aug 10 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92002167· OSTI ID:6917344

Awada, M A; Sin, S J ^[1]

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1. Florida Univ., Gainesville, FL (United States). Dept. of Physics

In this paper, the authors give a connection between the D = 1 matrix model and the generalized KP hierarchy. First, the authors find a difference equation satisfied by F, the Legendre transformation of the free energy of the D = 1 matrix model on a circle of radius R. Then the authors show that it is a special case of the difference equation of the generalized KP hierarchy with its zero mode identified with the scaling variable of the D = 1 string theory. The authors propose that the massive D = 1 matrix model is described by the generalized KP hierarchy, which implies the manifest integrability of D = 1 string theory. The authors also show that the (generalized) KP hierarchy has an underlying W[sub 1 + [infinity]] symmetry. By reduction, we prove that the generalized KdV hierarchy has a subalgebra of the above symmetry which again forms a W[sub 1+ [infinity]]. The authors argue that there are no W constraints in D = 1 string theory, which is in contrast to D [lt] 1 theories, where there are W[sub 1 + [infinity]] constraints.

• OSTI ID: 6917344
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:20; ISSN IMPAEF; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (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
ALGEBRA
COMPOSITE MODELS
CONFORMAL GROUPS
CONSTRAINTS
ENERGY
EXTENDED PARTICLE MODEL
FIELD THEORIES
FREE ENERGY
FUNCTIONS
LEGENDRE POLYNOMIALS
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICS
MATRICES
ONE-DIMENSIONAL CALCULATIONS
PARTICLE MODELS
PHYSICAL PROPERTIES
POLYNOMIALS
QUARK MODEL
SCALING LAWS
STRING MODELS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES
TRANSFORMATIONS