Related papers: Liouville bootstrap via harmonic analysis on a non…
We present a mechanism to construct four-dimensional charged massless Ramond states using the discrete states of a fivebrane Liouville internal conformal field theory. This conformal field theory has background charge, and admits an inner…
We consider timelike Liouville theory with FZZT-like boundary conditions. The bulk one-point and boundary two-point structure constants on a disk are derived using bootstrap. We find that these structure constants are not the analytic…
We develop a quantitative theory of Lipschitz harmonic functions (LHF) on finitely generated groups, with emphasis on the Lipschitz Liouville property, affine rigidity, and quasi-isometric invariance for groups of polynomial growth. On…
In this paper we study the rigidity problem for sub-static systems with possibly non-empty boundary. First, we get local and global splitting theorems by assuming the existence of suitable compact minimal hypersurfaces, complementing recent…
In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $\omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for…
We apply Kovacic's algorithm from differential Galois theory to show that all complex non-oscillatory solutions (finite exponential of convergence of zeros) of certain Hill equations considered by Bank and Laine using Nevanlinna theory must…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
A new approximate solution to the quantum-classical Liouville equation is derived starting from the formal solution of this equation in forward-backward form. The time evolution of a mixed quantum-classical system described by this equation…
We present a general method of solving the Cauchy problem for multidimensional parabolic (diffusion type) equation with variable coefficients which depend on spatial variable but do not change over time. We assume the existence of the…
In this work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT). We use the equations of motion to develop an analogue of the conformal block expansion for…
An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of…
We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…
In this work we derive braid group representations and Stokes matrices for Liouville conformal blocks with one irregular operator. By employing the Coulomb gas formalism, the corresponding conformal blocks can be interpreted as…
Liouville field theory is considered on domains with conformally invariant boundary conditions. We present an explicit expression for the three point function of boundary fields in terms of the fusion coefficients which determine the…
We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for random elliptic operators, our interest is in the…
In this note we derive large-scale regularity properties of solutions to second-order linear elliptic equations with random coefficients on the half- space with homogeneous Neumann boundary data; it is a companion to arXiv:1604.02717 in…
In this paper, we study the following system \begin{eqnarray*} \left\{ \begin{array}{ll} -\Delta u + V(x)u-(2\omega+\phi)\phi u=\lambda f(u)+|u|^{4}u, \ & \text{in} \ \mathbb{R}^{3}, \Delta \phi + \beta\Delta_4\phi = 4\pi(\omega+\phi)…
Liouville field theory on the pseudosphere is considered (Dirichlet conditions). We compute explicitely the bulk-boundary structure constant with two different methods: first we use a suggestion made by Hosomichi in JHEP 0111 (2001) that…
This work studies Liouville conformal blocks of irregular type with the insertion of at least one level-$3$ degenerate field admitting a Fibonacci fusion rule. We algebraically derive the corresponding third-order BPZ equations for regular…
We enlarge the spectral problem of a generalized D-Kaup-Newell (D-KN) spectral problem. Solving the enlarged zero-curvature equations, we produce integrable couplings. A reduction of the spectral matrix leads to a second integrable coupling…