Related papers: Modular Integrals in Minimal Super Liouville Gravi…
This paper elaborates on the bulk/boundary relation between negative cosmological constant 3D gravity and Liouville field theory (LFT). We develop an interpretation of LFT non-normalizable states in terms of particles moving in the bulk.…
It was shown recently that, beside the traditional Liouville action, other functionals appear in the gravitational action of two-dimensional quantum gravity in the conformal gauge, the most important one being the Mabuchi functional. In a…
We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the A_q integrable hierarchy via the resonance transformations, which are in turn…
We present for the first time the component structure of the supersymmetric completions for all curvature-squared invariants of five-dimensional, off-shell (gauged) minimal supergravity, including all fermions. This is achieved by using an…
This article carries out a qualitative analysis on a system of integral equations of the Hardy--Sobolev type. Namely, results concerning Liouville type properties and the fast and slow decay rates of positive solutions for the system are…
We discuss the relation between Liouville theory and the Hitchin integrable system, which can be seen in two ways as a two step process involving quantization and hyperkaehler rotation. The modular duality of Liouville theory and the…
We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to $c=1$ matter. Our motivation is to understand whether some form of…
In this note we derive an explicit modular invariant formula for the two loop 4-point amplitude in superstring theory in terms of a multiple integral (7 complex integration variables) over the complex plane which is shown to be convergent.…
We propose a precise duality between pure de Sitter quantum gravity in 2+1 dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arrive…
We present an interesting reformulation of a collection of dilaton gravity models in two space-time dimensions into a field theory of two decoupled Liouville fields in flat space, in the presence of a Maxwell gauge field. An effective…
The analytic structures of scattering amplitudes in gauge theory and gravity are examined on the celestial sphere. The celestial amplitudes in the two theories - computed by employing a regulated Mellin transform - can be compared at low…
We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the ${\cal N} = 4$ $SU(N)$ super-Yang-Mills theory, in the limit where $N$ is taken to be large while the complexified Yang-Mills…
Liouville field theory on hyperelliptic surface is considered. The partition function of the Liouville field theory on the hyperelliptic surface are expressed as a correlation function of the Liouville vertex operators on a sphere and the…
Some approaches to $2d$ gravity developed for the last years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. A special attention is paid to matrix models and their interrelations with different…
We investigate the moduli space of sheaves supported on space curves of degree 4 and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.
We study Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral quartic in momenta. The main results of the work are local description of such metrics in terms of…
We show that Liouville gravity arises as the limit of pure Einstein gravity in 2+epsilon dimensions as epsilon goes to zero, provided Newton's constant scales with epsilon. Our procedure - spherical reduction, dualization, limit, dualizing…
The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…
We are concerned with super-Liouville equations on the two sphere, which have variational structure with a strongly-indefinite functional. We prove the existence of non-trivial solutions by combining the use of Nehari manifolds, balancing…
The scalar one-loop 4-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method a characteristic scale $\mu_{s}$ is introduced to regularize the divergent…