Related papers: Conformal welding for critical Liouville quantum g…
We present a new holographic duality between q-Schwarzian quantum mechanics and Liouville gravity. The q-Schwarzian is a one parameter deformation of the Schwarzian, which is dual to JT gravity and describes the low energy sector of SYK. We…
The theory described by the sum of the Einstein-Hilbert action and the action of conformal scalar field possesses the duality symmetry which includes some special conformal transformation of the metric, and also inversion of scalar field…
We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite…
For Brownian surfaces with boundary and an interior marked point, a natural observable to consider is the distance profile, defined as the process of distances from the marked point to a variable point $x$ lying on the boundary. When the…
The quantum geometric tensor (QGT) provides nontrivial bounds among physical quantities, as exemplified by the metric-curvature inequality. In this paper, we investigate various bounds for different observables through certain…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a compact Riemann surface. We express this gravitational action in terms of finite and well-defined quantities for any value…
Quantization of two-dimensional dilaton gravity coupled to conformal matter is investigated. Working in conformal gauge about a fixed background metric, the theory may be viewed as a sigma model whose target space is parameterized by the…
We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle. The homeomorphism is constructed using the exponential of $\beta X$ where $X$ is the restriction of the…
We study the volume of metric balls in Liouville quantum gravity (LQG). For $\gamma \in (0,2)$, it has been known since the early work of Kahane (1985) and Molchan (1996) that the LQG volume of Euclidean balls has finite moments exactly for…
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…
Liouville quantum gravity (LQG) surfaces are a family of random fractal surfaces which can be thought of as the canonical models of random two-dimensional Riemannian manifolds, in the same sense that Brownian motion is the canonical model…
We derive the conformal Ward identities for the correlation functions of the Stress--Energy tensor in probabilistic Liouville Conformal Field Theory on compact Riemann surfaces by varying the correlation functions with respect to the…
Conformal algebra on R x S^3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless…
We consider conformal defect solutions in four dimensional $N=2$ gauged supergravity. These solutions are constructed as a warped product of $AdS_2\times S^1$ over an interval with non-trivial electric and magnetic fields. We show for…
The consistent embedding of Loop Quantum Gravity (LQG) effects within the Standard Model requires a rigorous understanding of how Planck-scale deformations manifest at low energies. While phenomenological approaches often introduce…
We study a limit in which a relativistic CFT reduces to conformal quantum mechanics, and relate the partition functions of the two theories. When the initial CFT is holographic, our limit coincides with an ultra-spinning limit in the…
This paper is concerned with computing the spectral dimension of 2d-Liouville quantum gravity. As a warm-up, we first treat the simple case of boundary Liouville quantum gravity. We prove that the spectral dimension is 1 via an exact…
Flat-space conformal invariance and curved-space Weyl invariance are simply related in dimensions greater than two. In two dimensions the Liouville theory presents an exceptional situation, which we here examine.
In this paper, we prove the following two results: First, we study a class of conformally invariant operators $P$ and their related conformally invariant curvatures $Q$ on even-dimensional Riemannian manifolds. When the manifold is locally…