Related papers: Differential equation for four-point correlation f…
We present an explicit momentum space computation of the four-point function of the energy-momentum tensor in 4 spacetime dimensions for the free and conformally invariant theory of a scalar field. The result is obtained by explicit…
We propose a correction to one of the elliptic blocks in the NS sector of 2d $\mathcal N = 1$ superconformal field theories. We analyze the 4-point block in the pillow geometry to demonstrate the necessity of the correction and verify the…
We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…
The well-known modular property of the torus characters and torus partition functions of (rational) vertex operator algebras (VOAs) and 2d conformal field theories (CFTs) has been an invaluable tool for studying this class of theories. In…
It is known that the path integral of correlators in Liouville theory reduces to a finite dimensional integral in the limit of vanishing coupling b. We take the example of four-point functions on sphere and investigate how the simple…
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…
Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view…
In this work we initiate an integrability-based approach to multipoint conformal blocks for higher dimensional conformal field theories. Our main observation is that conformal blocks for $N$-point functions may be considered as…
The correlation functions for models of minimal gravity are discussed. An algorithm is proposed for calculations of invariant ratios from formulas of residues that can be compared with the coefficients of expansion of the partition function…
In this article, we will show how to use Zamolodchikov's higher equations of motion in Liouville field theory to explicitly calculate $N$-point correlation numbers in minimal Liouville gravity for $N>4$. We find the explicit expression for…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
Liouville conformal field theory is considered with conformal boundary. There is a family of conformal boundary conditions parameterized by the boundary cosmological constant, so that observables depend on the dimensional ratios of boundary…
Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Here, we study Liouville conformal field theory in the classical (large central charge) limit, where it encodes the geometry of the moduli…
The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with $SL(2,\mathbb{C})$-valued monodromy on Riemann surfaces of genus zero with $n$ punctures can be solved by taking suitable linear…
We use the correspondence between scalar field theory on $AdS_{d+1}$ and a conformal field theory on $R^d$ to calculate the 3- and 4-point functions of the latter. The classical scalar field theory action is evaluated at tree level.
We calculate a class of two-point boundary correlators in 2D quantum gravity using its microscopic realization as loop gas on a random surface. We find a perfect agreement with the two-point boundary correlation function in Liouville…
We study the gluing theory of Riemann surfaces using formal algebraic geometry, and give computable relations between the associated parameters for different gluing processes. As its application to the Liouville conformal field theory, we…
We calculate the four point correlation function for scalar perturbations in the canonical model of slow-roll inflation. We work in the leading slow-roll approximation where the calculation can be done in de Sitter space. Our calculation…
We propose an exact form of the fusion matrix of the Neveu-Schwarz blocks that appear in a correlation function of four super-primary fields. Orthogonality relation satisfied by this matrix is equivalent to the bootstrap equation for the…
The purpose of these notes, based on a series of 4 lectures given by the author at IHES, is to explain the recent proof of the DOZZ formula for the three point correlation functions of Liouville conformal field theory (LCFT). We first…