Journal ArticleDOI
Diseases of triangulated random surface models, and possible cures
TLDR
The results uncover new difficulties in quantizing and regularizing the Nambu-Goto string and a new class of random surface models with more coercive actions are proposed which are expected to have improved behaviour and appear to be accessible to numerical simulations.About:
This article is published in Nuclear Physics.The article was published on 1985-01-01. It has received 581 citations till now.read more
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Random-matrix theories in quantum physics : common concepts
TL;DR: A review of the development of random-matrix theory (RMT) during the last fifteen years is given in this paper, with a brief historical survey of the developments of RMT and of localization theory since their inception.
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Random Matrix Theories in Quantum Physics: Common Concepts
TL;DR: It is suggested that the current development of random-matrix theory signals the emergence of a new “statistical mechanics”: Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.
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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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Topological field theory
References
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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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Quantum field theory techniques in graphical enumeration
TL;DR: In this article, a method for counting closed graphs on a compact Riemannian surface based on techniques suggested by quantum field theory is presented. But this method is not suitable for counting graphs on Riemans.
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Infrared Bounds, Phase Transitions and Continuous Symmetry Breaking
TL;DR: In this article, it was shown that phase transitions occur in (φ·φ) 3 2 quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions.
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Dual-resonance models
TL;DR: In this article, the dual-resonance model is treated both as S -matrix theories and as systems of interacting strings, and the related questions of ghost elimination and null states are discussed.
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Critical behaviour in a model of planar random surfaces
TL;DR: In this article, the authors show that the string tension does not tend to zero at a critical point in a planar random surface model with the assumption that the susceptibility diverges at the critical point.