Related papers: On two-dimensional quantum gravity and quasiclassi…

In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…

String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string…

The theory of embedded random surfaces, equivalent to two--dimensional quantum gravity coupled to matter, is reviewed, further developed and partly generalized to four dimensions. It is shown that the action of the Liouville field theory…

In this thesis special emphasis is put on the quantization of the spherically reduced Einstein-massless-Klein-Gordon model using a first order approach for geometric quantities, because phenomenologically it is probably the most relevant of…

I investigate two discrete models of random geometries, namely simplicial quantum gravity and quantum string theory. In four-dimensional simplicial quantum gravity, I show that the addition of matter gauge fields to the model is capable of…

We propose a new approach to the quasitopological theory of gravity based on a modified classical double--copy construction. Focusing on static, spherically symmetric configurations, we show that all vacuum solutions of $D$--dimensional…

This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…

We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and…

We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the…

Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum…

We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy…

We consider the theory of pure gravity in 2+1 dimensions, with negative cosmological constant. The theory contains simple matter in the form of point particles; the later are classically described as lines of conical singularities. We…

We describe an approach to the quantisation of (2+1)-dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q-commutation relation. Solutions of diagonal and…

In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of…

We re-examine results of the Liouville theory and provide arguments that a {\it negative} bare cosmological constant is essential to define two-dimensional quantum gravity. From this we are naturally led to a regularization of quantum…

An assessment is offered of the progress that the major approaches to quantum gravity have made towards the goal of constructing a complete and satisfactory theory. The emphasis is on loop quantum gravity and string theory, although other…

We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…

The three-point functions for minimal models coupled to gravity are derived in the operator approach to Liouville theory which is based on its $U_q(sl(2))$ quantum group structure. The result is shown to agree with matrix-model calculations…

We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…

Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of…