Related papers: Liouville Quantum Gravity on the unit disk
First passage percolation (FPP) on $\mathbb{Z}^d$ or $\mathbb{R}^d$ is a canonical model of a random metric space where the standard Euclidean geometry is distorted by random noise. Of central interest is the length and the geometry of the…
Motivated by the question of exploring the "theory space" of quantum field theories, we review the concept of "decomposing" and "gluing" quantum field theories. We explain this in the context of three-dimensional $\mathcal{N}=2$…
In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3+1 space-time dimensions, the boundary theory lives on the 2+1-dimensional…
We consider the singular Liouville equation and the Henon-Lane-Emden problem on simply connected planar domains. We show that any solution to each problem must satisfy a uniform bound on the mass. The same results applies to some systems…
We propose an unified theory for spinor fields on extended Weyl manifolds taking into account self-interactions to obtain the Relativistic dynamics on a general curved Riemannian background as continuation of the Relativistic Quantum…
The Liouville action emerges as the effective action of 2-d gravity in the process of path integral quantization of the bosonic string. It yields a measure of the violation of classical symmetries of the theory at the quantum level. Certain…
In this paper we establish a fractional generalization of Einstein field equations based on the Riemann-Liouville fractional generalization of the ordinary differential operator $\partial_\mu$. We show some elementary properties and prove…
We obtain exact formulae for three basic quantities in random conformal geometry that depend on the modulus of an annulus. The first is for the law of the modulus of the Brownian annulus describing the scaling limit of uniformly sampled…
In any dimension $D$, the Euclidean Einstein-Hilbert action, which describes gravity in the absence of matter, can be discretized over random discrete spaces obtained by gluing families of polytopes together in all possible ways. In the…
By compactifying gauge theories on a lower dimensional manifold, we often find many interesting relationships between a geometry and a supersymmetric quantum field theory. In this paper we consider conformal field theories obtained from…
In the quantum Teichmuller theory, based on Penner coordinates, the mapping class groups of punctured surfaces are represented projectively. The case of a genus three surface with one puncture is worked out explicitly. The projective factor…
Given a planar continuum Gaussian free field $h^{\mathcal U}$ in a domain $\mathcal U$ with Dirichlet boundary condition and any $\delta>0$, we let $\{h_\delta^{\mathcal U}(v): v\in \mathcal U\}$ be a real-valued smooth Gaussian process…
The path integral of four dimensional quantum gravity is restricted to conformally self-dual metrics. It reduces to integrals over the conformal factor and over the moduli space of conformally self--dual metrics and can be studied with the…
In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a…
We present a nonperturbative field theoretic method based on the Liouville-Neumann (LN) equation. The LN approach provides a unified formulation of nonperturbative quantum fields and also nonequilibrium quantum fields, which makes use of…
We propose a method to construct quantum theory of matter fields in a topology changing universe. Analytic continuation of the semiclassical gravity of a Lorentzian geometry leads to a non-unitary Schr\"{o}dinger equation in a Euclidean…
We show that Liouville gravity arises as the limit of pure Einstein gravity in 2+epsilon dimensions as epsilon goes to zero, provided Newton's constant scales with epsilon. Our procedure - spherical reduction, dualization, limit, dualizing…
The bootstrap for Liouville theory with conformally invariant boundary conditions will be discussed. After reviewing some results on one- and boundary two-point functions we discuss some analogue of the Cardy condition linking these data.…
In this talk I review some of the recent developments in the field of random surfaces and the Dynamical Triangulation approach to simplicial quantum gravity. In two dimensions I focus on the c=1 barrier and the fractal dimension of…
We give a short and rigorous proof of the existence and uniqueness of the solution of Liouville equation with sources, both elliptic and parabolic, on the sphere and on all higher genus compact Riemann surfaces.