Abstract
This paper gives a brief introduction to using two-dimensional discrete and Euclidean quantum gravity approaches as a laboratory for studying the properties of fluctuating and frozen random graphs in interaction with “matter fields” represented by simple spin or vertex models. Due to the existence of numerous exact analytical results and predictions for comparison with simulational work, this is an interesting and useful enterprise.
Highlights
Field theoretical formulations of Einstein gravity are known to be perturbatively non-renormalizable
The Regge formulation of quantum gravity [2,7] stays relatively close to the continuum formulation, which for instance for two-dimensional (2D) Euclidean R2-gravity would be defined through the partition function
The field-theory ansatz leading to equation (11) breaks down for central charges C > 1, an effect which has been termed the C = 1 “barrier”, whereas discrete models of C > 1 matter coupled to dynamical triangulations or quadrangulations still appear to be well-defined
Summary
Field theoretical formulations of Einstein gravity are known to be perturbatively non-renormalizable. In the dynamical triangulations model, on the other hand, the situation is reversed: here the edge lengths are kept fixed, but the connectivities are allowed to vary dynamically from vertex to vertex [6] This latter case allows for exact solutions. After a brief introduction to the two formulations of two-dimensional Euclidean quantum gravity, this paper will focus on the statistical physics interpretation of spin and vertex models coupled to fluctuating or quenched quantum gravity graphs. Both analytical and numerical results will be discussed and compared with each other
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
