Related papers: From Quantum Groups to Liouville and Dilaton Quant…
After reviewing the algebraic structures that underlie the geometries of N=2 Maxwell-Einstein supergravity theories (MESGT) in five and four dimensions with symmetric scalar manifolds, we give a unified realization of their three…
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…
We investigate Liouville-type results, existence, uniqueness and symmetry to the solution of nonlinear nonlocal elliptic equations of the form \[ Lu = |x|^{\gamma}\,H(u)\,G(\nabla u), \qquad x\in\R^n, \] where $L$ is a symmetric,…
Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability theory and mathematical physics in the past two decades. In this proceeding, we review two aspects of this topic. The first is…
An open issue in loop quantum gravity (LQG) is the introduction of a non-vanishing cosmological constant $\Lambda$. In 3d, Chern-Simons theory provides some guiding lines: $\Lambda$ appears in the quantum deformation of the gauge group. The…
It has been often observed that K\"ahler geometry is essentially a $U(1)$ gauge theory whose field strength is identified with the K\"ahler form. However it has been pursued neither seriously nor deeply. We argue that this remarkable…
Liouville Field Theory (LFT for short) is a two dimensional model of random surfaces, which is for instance involved in $2d$ string theory or in the description of the fluctuations of metrics in $2d$ Liouville quantum gravity. This is a…
In the series of papers we represent the ``Whittaker'' wave functional of $d+1$-dimensional Liouville model as a correlator in $d+0$-dimensional theory of the sine-Gordon type (for $d=0$ and $1$). Asypmtotics of this wave function is…
We present a rigorous framework for determining equilibrium configurations of uniformly rotating self-gravitating fluid bodies. This work addresses the longstanding challenge of modeling rotational deformation in celestial objects such as…
We present a short review of the group-geometric approach to supergravity theories, from the point of view of recent developments. The central idea is the unification of usual diffeomorphisms, gauge symmetries and supersymmetries into…
Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…
We shed a new light on the $L^1$-Liouville property for positive, superharmonic functions by providing many evidences that its validity relies on geometric conditions localized on large enough portions of the space. We also present examples…
We introduce an $N=1$ supergravity model based on the gauged shift symmetry of a single chiral multiplet, which can be identified with the string dilaton or a compactification modulus. The model allows for a tunably small and positive value…
Let $U_\varepsilon({\mathfrak g})$ be the standard simply connected version of the Drinfeld-Jumbo quantum group at an odd primitive m-th root of unity $\varepsilon$. The center of $U_\varepsilon({\mathfrak g})$ contains a huge commutative…
We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of elliptic elements to the classical Liouville action is derived in terms of the…
The quantum dynamics of a particle in the Modified P\"oschl-Teller potential is derived from the group $SL(2,R)$ by applying a Group Approach to Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder operators is…
The symplectic and Poisson structures of the Liouville theory are derived from the symplectic form of the SL(2,R) WZNW theory by gauge invariant Hamiltonian reduction. Causal non-equal time Poisson brackets for a Liouville field are…
In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov. Our approach follows the construction carried out by the authors together with A. Kupiainen in…
A detailed reexamination is made of the exact operator formalism of two-dimensional Liouville quantum gravity in Minkowski spacetime with the cosmological term fully taken into account. Making use of the canonical mapping from the…
We review the group-geometric approach to supergravity theories, in the perspective of recent developments and applications. Usual diffeomorphisms, gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a supergroup…