Two-dimensional quantum gravity, matrix models and string theory

Miscellaneous · Wed Jan 01 00:00:00 EST 1992

OSTI ID:6972718

Demeterfi, K

A detailed review of simple models of two-dimensional quantum gravity and non-critical string theories is presented. The author describes the lattice formulation of various models of 2D quantum gravity and their equivalence to some matrix field theories. The 1/N expansion of the matrix model (N being the size of the matrix) corresponds to the perturbative expansion of string theory in the coupling constant g[sup 0][sub st] [identical to] 1/N. The singularity of the matrix model free energy is enhanced at every subsequent order in the 1/N expansion in a systematic way. This leads to the definition of the double-scaling limit, in which the entire topological expansion can be summed up in a differential equation for the string susceptibility. These features are illustrated on the example of the one-matrix model. The generalization to multimatrix models is briefly described. An elementary discussion is given of the phase structure of matrix models and it is shown that the double-scaling limit in different phases leads to different string equations. The author presents the semiclassical solution of a one-dimensional matrix model which represents the Polyakov string moving in one dimension. The new phenomenon of logarithmic scaling violation is emphasized. The field theoretic formulation of the model is achieved through the collective field method. This approach leads to a two-dimensional massless scalar field theory which describes the dynamics of tachyons and explains the scaling-violating terms. A systematic perturbative expansion is developed for the collective field theory. In addition to the massless tachyon an infinite set of states with discrete momenta is manifest in the integral representation of the scattering amplitude. The author discusses the computation of the tachyon scattering amplitudes in Louiville theory and compares it with the collective field theory.

• Research Organization: Brown Univ., Providence, RI (United States)
• OSTI ID: 6972718
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM GRAVITY
LATTICE FIELD THEORY
TWO-DIMENSIONAL CALCULATIONS
STRING MODELS
REVIEWS
LIOUVILLE THEOREM
TACHYONS
COMPOSITE MODELS
DOCUMENT TYPES
ELEMENTARY PARTICLES
EXTENDED PARTICLE MODEL
FIELD THEORIES
MATHEMATICAL MODELS
PARTICLE MODELS
POSTULATED PARTICLES
QUANTUM FIELD THEORY
QUARK MODEL
661310* - Relativity & Gravitation- (1992-)
662110 - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)