相关论文: Critical Liouville quantum gravity and CLE$_4$

General properties of perturbed conformal field theory interacting with quantized Liouville gravity are considered in the simplest case of spherical topology. We discuss both short distance and large distance asymptotic of the partition…

It is shown that conformal matter with $c_{\ssc L}\not=c_{\ssc R}$ can be consistently coupled to two-dimensional `frame' gravity. The theory is quantized, following David, and Distler and Kawai, using the derivation of their {\it ansatz}…

We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. The limit is an LQG harmonic ball, which we constructed in a…

Discrete and continuum Liouville first passage percolation (DLFPP, LFPP) are two approximations of the conjectural $\gamma$-Liouville quantum gravity (LQG) metric, obtained by exponentiating the discrete Gaussian free field (GFF) and the…

The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for…

Inspired by Polyakov's original formulation of quantum Liouville theory through functional integral, we analyze perturbation expansion around a classical solution. We show the validity of conformal Ward identities for puncture operators and…

Liouville first passage percolation (LFPP) with parameter $\xi >0$ is the family of random distance functions $\{D_h^\epsilon\}_{\epsilon >0}$ on the plane obtained by integrating $e^{\xi h_\epsilon}$ along paths, where $h_\epsilon$ for…

A rigorous probabilistic construction of Liouville conformal field theory (LCFT) on the Riemann sphere was recently given by David-Kupiainen and the last two authors. In this paper, we focus on the connection between LCFT and the classical…

Let $\gamma \in (0,2)$, let $h$ be the planar Gaussian free field, and consider the $\gamma$-Liouville quantum gravity (LQG) metric associated with $h$. We show that the essential supremum of the Hausdorff dimension of the boundary of a…

As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…

We show that under certain technical assumptions, including the existence of a constant mean curvature (CMC) slice and strict positivity of the scalar field, general relativity conformally coupled to a scalar field can be quantised on a…

Two desireable properties of a quantum dynamics for Loop Quantum Gravity (LQG) are that its generators provide an anomaly free representation of the classical constraint algebra and that physical states which lie in the kernel of these…

An explicit construction for the monodromy of the Liouville conformal blocks in terms of Racah-Wigner coefficients of the quantum group U_q(sl(2,R)) is proposed. As a consequence, crossing-symmetry for four point functions is analytically…

We investigate the quantum Lifshitz criticality in a general background of Einstein-Maxwell-Dilaton gravity. In particular, we demonstrate the existence of critical point with dynamic critical exponent z by tuning a nonminimal coupling to…

Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL(2,C). Even though many monographs exist devoted to this theory, the different tools needed (e.g. representation theory, harmonic…

We endow the $\sqrt{8/3}$-Liouville quantum gravity sphere with a metric space structure and show that the resulting metric measure space agrees in law with the Brownian map. Recall that a Liouville quantum gravity sphere is a priori…

It is well known that the quantum double structure plays an important role in three dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three dimensional…

Motivated by the works on Equivalence Principle in the context of linear Generalized Uncertainty Principle and, independently, in the context of quadratic Generalized Uncertainty Principle, we expand these endeavors in the context of…

We study the quantum aspects of the conformal gravity in four dimensions, specifically addressing a known discrepancy in beta functions between general quadratic curvature theories and conformal gravity, which corresponds to two scalar…

Loop Quantum Gravity (LQG) is a theory that proposes a way to model the behavior of the spacetime in situations where its atomic characteristic arises. Among these situations, the spacetime behavior near the Big Bang or black hole's…