8 research outputs found
From 1-matrix model to Kontsevich model
Loop equations of matrix models express the invariance of the models under
field redefinitions. We use loop equations to prove that it is possible to
define continuum times for the generic hermitian {1-matrix} model such that all
correlation functions in the double scaling limit agree with the corresponding
correlation functions of the Kontsevich model expressed in terms of kdV times.
In addition the double scaling limit of the partition function of the hermitian
matrix model agree with the -function of the kdV hierarchy corresponding
to the Kontsevich model (and not the square of the -function) except for
some complications at genus zero.Comment: 17 pages, Late
Quantum Gravity, Dynamical Triangulation and Higer Derivative Regularization
We consider a discrete model of euclidean quantum gravity in four dimensions
based on a summation over random simplicial manifolds. The action used is the
Einstein-Hilbert action plus an -term. The phase diagram as a function of
the bare coupling constants is studied in the search for a sensible continuum
limit. For small values of the coupling constant of the term the model
seems to belong to the same universality class as the model with pure
Einstein-Hilbert action and exhibits the same phase transition. The order of
the transition may be second or higher. The average curvature is positive at
the phase transition, which makes it difficult to understand the possible
scaling relations of the model.Comment: 27 pages (Latex), figures not included. Post script file containing
15 figures (1000 blocks) available from [email protected]
Review of AdS/CFT Integrability: An Overview
This is the introductory chapter of a review collection on integrability in
the context of the AdS/CFT correspondence. In the collection we present an
overview of the achievements and the status of this subject as of the year
2010.Comment: 31 pages, v2: reference added, references to other chapters updated,
v3: footnote 1 on location of references added, v4: minor changes, references
added, accepted for publication in Lett. Math. Phys, v5: minor corrections,
links to chapters updated, attached IntAdS.pdf with all chapters in one file,
see http://arxiv.org/src/1012.3982/anc/IntAdS.pdf or
http://www.phys.ethz.ch/~nbeisert/IntAdS.pd
Review of AdS/CFT Integrability
This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection we present an overview of the achievements and the status of this subject as of the year 2010