Related papers: Duality and KPZ in Liouville Quantum Gravity
The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q)…
We re-examine the nonperturbative curvature properties of two-dimensional Euclidean quantum gravity, obtained as the scaling limit of a path integral over dynamical triangulations of a two-sphere, which lies in the same universality class…
We investigate the underlying quantum group symmetry of 2d Liouville and dilaton gravity models, both consolidating known results and extending them to the cases with $\mathcal{N} = 1$ supersymmetry. We first calculate the mixed parabolic…
Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal surfaces which first appeared in the physics literature in the 1980s. Recent works have constructed a metric (distance function) on an LQG surface. We…
We study the extremal process associated with the Discrete Gaussian Free Field on the square lattice and elucidate how the conformal symmetries manifest themselves in the scaling limit. Specifically, we prove that the joint process of…
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…
In order to study the quantum geometry of random surfaces in Liouville gravity, we propose a definition of geodesic distance associated to a Gaussian free field on a regular lattice. This geodesic distance is used to numerically determine…
Quantum theory of dilaton gravity is studied in $2+\epsilon$ dimensions. Divergences are computed and renormalized at one-loop order. The mixing between the Liouville field and the dilaton field eliminates $1/\epsilon$ singularity in the…
We construct and analyze conformally invariant random fields on 4-dimensional Riemannian manifolds $(M,g)$. These centered Gaussian fields $h$, called \emph{co-biharmonic Gaussian fields}, are characterized by their covariance kernels $k$…
$\gamma$-Liouville quantum gravity ($\gamma$-LQG) constitutes a family of planar random geometries whose geodesics exhibit intricate fractal behaviour. As is observed in various planar models of random geometry as part of the phenomenon of…
We examine a possibility to introduce a non-trivial classical background metric into the 2-d Liouville gravity theory. The classical background appears as a part of the Weyl factor of the physical metric of 2-d surfaces with some conformal…
The origin of the rather mysterious duality symmetry found in quantum Liouville theory is investigated by considering the Liouville theory as the reduction of a WZW-like theory in which the form of the potential for the Cartan field is not…
We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which corresponds to central charge values $\mathbf c_{\mathrm L} \in…
We study a new two-dimensional quantum gravity theory, based on a gravitational action containing both the familiar Liouville term and the Mabuchi functional, which has been shown to be related to the coupling of non-conformal matter to…
2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in the realm of probability theory: David,…
We study pure 2D Euclidean quantum gravity with $R^2$ interaction on spherical lattices, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size scaling Ansatz in the…
Consider a critical ($\gamma=2$) Liouville quantum gravity (LQG) disk together with an independent conformal loop ensemble (CLE) with parameter $\kappa=4$. We show that the critical LQG surfaces parametrized by the regions enclosed by the…
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…
We study Liouville quantum gravity (LQG) surfaces whose law has been reweighted according to nesting statistics for a conformal loop ensemble (CLE) relative to $n\in \mathbb{N}_0$ marked points $z_1,\dots,z_n$. The idea is to consider a…
We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere $SU_q (2)/U(1) $. The $SU_q (2)$-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group…