Related papers: Simple Conformal Loop Ensembles on Liouville Quant…
We derive the Ward identities of Conformal Field Theory (CFT) within the framework of Schramm-Loewner Evolution (SLE) and some related processes. This result, inspired by the observation that particular events of SLE have the correct…
We showed that the SLE bubble measure recently constructed by Zhan arises naturally from the conformal welding of two Liouville quantum gravity (LQG) disks. The proof relies on (1) a "quantum version" of the limiting construction of the SLE…
In the path integral formulation of the reduced phase space Loop Quantum Gravity (LQG), we propose a new approach to allow the spatial cubic lattice (graph) to change dynamically in the physical time evolution. The equations of motion of…
This manuscript explores the connections between a class of stochastic processes called "Stochastic Loewner Evolution" (SLE) and conformal field theory (CFT). First some important results are recalled which we utilise in the sequel, in…
We investigate the universal behaviour of a one-parameter generalisation of the six-vertex model on planar graphs, which we refer to as the seven-vertex model, or 7vM for quick reference. The 7vM is characterised by a temperature coupling…
We study small time bounds for transition densities of convolution semigroups corresponding to pure jump L\'evy processes in $\mathbb{R}^{d}$, $d \geq 1$, including those with jumping kernels exponentially and subexponentially localized at…
Let $(\mathscr{C}, \omega_{\mathscr{C}})$ be a Ricci-flat, simply connected, conical K\"ahler manifold. We establish a Liouville theorem for constant scalar curvature K\"ahler (cscK) metrics on $\mathscr{C}$. The theorem asserts that any…
We provide another construction of the natural parametrization of SLE$_\kappa$ for $\kappa < 4$. We construct it as the expectation of the quantum time, which is a random measure carried by SLE in an ambient Gaussian free field. This…
Liouville's theorem says that in dimension greater than two, all conformal maps are M\"obius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally…
We comment on structural properties of the algebras $\mathfrak{A}_{LQG/LQC}$ underlying loop quantum gravity and loop quantum cosmology, especially the representation theory, relating the appearance of the (dynamically induced)…
These are notes of a seminar given at the 30th International Symposium on the Theory of Elementary Particles, Berlin-Buckow, August 1996. The material is derived from collaborations with E. Cremmer and J.-L. Gervais, and C. Klimcik, and is…
Particular boundary correlation functions of conformal field theory are needed to answer some questions related to random conformally invariant curves known as Schramm-Loewner evolutions (SLE). In this article, we introduce a correspondence…
We find explicit formulas for the probabilities of general boundary visit events for planar loop-erased random walks, as well as connectivity events for branches in the uniform spanning tree. We show that both probabilities, when suitably…
We evaluate one loop quantum gravity corrections to the conformally coupled (CC) scalar self-mass-squared on a locally de Sitter background. In this paper we consider only the conformal-conformal interaction part of the self-mass-squared.…
The effective approach in Loop Quantum Cosmology (LQC) has provided means to obtain predictions for observable quantities in LQC models. While an effective dynamics in LQC has been extensively considered in different scenarios, a robust…
We construct the stress-energy tensor correlation functions in probabilistic Liouville Conformal Field Theory (LCFT) on the two-dimensional sphere by studying the variation of the LCFT correlation functions with respect to a smooth…
We examine the relations between observables in two- and three-dimensional quantum gravity by studying the coupling of topologically massive gravity to matter fields in non-trivial representations of the three-dimensional Lorentz group. We…
We review the derivation of the Liouville action in 2DQG via the trace anomaly and emphasize how a similar approach can be used to derive an effective action describing the long wavelength dynamics of the conformal factor in 4D. In 2D we…
In this article, we use the framework of "Random conformal weldings" (by K. Astala, P. Jones, A. Kupiainen, E. Saksman) to prove the existence of Lehto-welding for the inverse for $\gamma<0.1818$ and independent copies for…
Loop quantum gravity (LQG) is a quantization program for gravity based on the principles of QFT and general covariance of general relativity. Quantum states of LQG describe gravitational excitations based on graphs embedded in a spatial…