Related papers: Liouville theory without an action

We discuss some aspects of Liouville field theory, starting from operator equation of motion in presence of two screening charges and re-derive the dual zero mode Schwinger Dyson equations for the two screening charges from the path…

In this article we prove smoothness of the correlation functions in probabilistic Liouville Conformal Field Theory. Our result is a step towards proving that the correlation functions satisfy the higher Ward identities and the higher BPZ…

Consider a conformally covariant four-point function of identical scalar operators with a discrete spectrum, a twist gap, and compatible with the unitarity conditions. We give a mathematical proof confirming that the spectrum and OPE…

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 compute the super Liouville action for a two dimensional Regge surface by exploiting the invariance of the theory under the superconformal group for sphere topology and under the supermodular group for torus topology. For sphere topology…

We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a…

We introduce a new two-dimensional string theory defined by coupling two copies of Liouville CFT with complex central charge $c=13\pm i \lambda$ on the worldsheet. This string theory defines a novel, consistent and controllable model of…

Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of…

In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum…

We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a…

We construct the effective action and gap equations for nonperturbative fermion 4-point functions. Our results apply to situations in which fermion masses can be ignored, which is the case for theories of strong flavor interactions…

Liouville field theory is quantized by means of a Wilsonian effective action and its associated exact renormalization group equation. For $c<1$, an approximate solution of this equation is obtained by truncating the space of all action…

We derive a generating function for all the 3-point functions of higher spin conserved currents in four dimensional conformal field theory. The resulting expressions have a rather surprising factorized form which suggest that they can all…

The role played by the Euler anomaly in the dictionary relating sphere partition functions of four dimensional theories of class $\mathcal{S}$ and two dimensional nonrational CFTs is clarified. On the two dimensional side, this involves a…

In previous work we have shown that the (\theta->\infty)-limit of \phi^4_4-quantum field theory on noncommutative Moyal space is an exactly solvable matrix model. In this paper we translate these results to position space. We show that the…

We present a new, short and independent proof of the Liouville-type theorem for entire and subharmonic functions of finite order bounded outside some set of zero planar density.

Timelike Liouville field theory is a candidate model for positive curvature two-dimensional quantum gravity, but a mathematically controlled Lorentzian formulation has remained elusive. In this paper we construct the theory on the cylinder…

We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly regularizing the Green function. Explicit…

Using an rotation of Yuan, we observe that the gradient graph of any semiconvex function is a Liouville manifold, that is, does not admit bounded harmonic functions. As a corollary, we find that any entire solution of the fourth order…

We construct correlators in the $W_4$ Toda 2d conformal field theory for a particular class of representations and demonstrate a relation to a $W_2$ (Virasoro) theory with different central charge. The relevance of the classical limits of…