Journal ArticleDOI
Critical properties of randomly triangulated planar random surfaces
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In this article, a discrete version of the Polyakov string is studied by analytical and numerical methods, where the role of the intrinsic metric is played by random triangulation and the critical exponents for the solvable cases D = 0 and D = −2 are shown to be larger than those calculated perturbatively.About:
This article is published in Physics Letters B.The article was published on 1985-07-18. It has received 590 citations till now. The article focuses on the topics: Hausdorff dimension & Critical exponent.read more
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2D gravity and random matrices
TL;DR: In this article, the authors review recent progress in 2D gravity coupled to d < 1 conformal matter, based on a representation of discrete gravity in terms of random matrices and discuss the saddle point approximation for these models, including a class of related O(n) matrix models.
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Exactly Solvable Field Theories of Closed Strings
Edouard Brézin,Vladimir Kazakov +1 more
TL;DR: In this article, it was shown that the two-point function χ(λ,N), in which λ is the cosmological constant and N−1 is the string coupling constant, obeys a scaling law χ (λ, N=N −(m+1 2 ) ⨍((λ c −λ)N m/(m+ 1 2 ) ) in the limit in which n−1 goes to zero and λ goes to a critical value λc; this transition is a "condensation of handles" on the world sheet
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Conformal bootstrap in Liouville field theory
TL;DR: In this article, Liouville Field Theory (LFT) was shown to reproduce some of the predictions of the matrix model approach, in particular the scaling behavior, genus one partition functions, and integrated correlation functions.
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Topological field theory
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Invariants of algebraic curves and topological expansion
Bertrand Eynard,Nicolas Orantin +1 more
TL;DR: In this article, an infinite sequence of invariants for any algebraic curve is defined, which can be used to define a formal series, which satisfies formally an Hirota equation, and thus obtain a new way of constructing a tau function attached to an algebraic graph.
References
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Introduction to the theory of quantized fields
TL;DR: Shirkov as discussed by the authors gave a dierent perspective on the ordinary quantum theory of a single spinless, positive msss-m particle on Rd−1, and investigated a special case that relates to the Gaussian path integral and the free quantum eld.
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Quantum Geometry of Bosonic Strings
TL;DR: In this article, a formalism for computing sums over random surfaces which arise in all problems containing gauge invariance (like QCD, three-dimensional Ising model etc.) is developed.
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A two-dimensional model for mesons
TL;DR: In this paper, a recently proposed gauge theory for strong interactions, in which the set of planar diagrams play a dominant role, is considered in one space and one time dimension, and it can be reduced to self-energy and ladder diagrams, and they can be summed.
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Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary condition of dual resonance model
TL;DR: In this article, it was shown that the wave equation and subsidiary conditions found by Virasoro in the dual resonance model are equivalent to relativistic quantum mechanics in our system.
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Bilocal Regularization of Models of Random Surfaces
TL;DR: In this article, a new formulation of a Weingarten-type model in terms of bilocal (no-matrix) variables in continuous space is given, which is equivalent to the model of triangular planar random surfaces.