Related papers: Gauge/Liouville Triality
We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions…
Motivated by recent works on the connection between 2D quantum gravity and timelike Liouville theory, we revisit the latter and clarify some aspects of the computation of its partition function: We present a detailed computation of the…
In this note, we explore the relation between crossing symmetry and modular invariance in conformal field theory and S-duality in gauge theory. It is shown that partition functions of different S dual theories of N=2 SU(2) gauge theory with…
We investigate the relation between 3d N=2 theories and 2d free field correlators or Dotsenko-Fateev (DF) integrals for Liouville CFT. We show that the S^2xS^1 partition functions of some known 3d Seiberg-like dualities reduce, in a…
We review the derivation of the Liouville action in 2DQG via the trace anomaly and emphasize how a similar approach can be used to derive an effective action describing the long wavelength dynamics of the conformal factor in 4D. In 2D we…
We compute the disk 1-point function in timelike Liouville theory. Using the Coulomb gas formalism and analytically continuing in the number of screening operators, we derive an explicit formula, which is shown to satisfy the correct…
We calculate three- and four-point functions in super Liouville theory coupled to super Coulomb gas on world sheets with spherical topology. We first integrate over the zero mode and assume that a parameter takes an integer value. After…
We develop a perturbative expansion of quantum Liouville theory on the pseudosphere around the background generated by heavy charges. Explicit results are presented for the one and two point functions corresponding to the summation of…
It is shown that the two dimensional gravity, described either in the conformal gauge (the Liouville theory) or in the light cone gauge, when coupled to matter possesses an infinite number of twisted $N=2$ superconformal symmetries. The…
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to…
Timelike Liouville field theory (also known as imaginary Liouville theory or imaginary Gaussian multiplicative chaos) is expected to describe two-dimensional quantum gravity in a positive-curvature regime, but its path integral is not a…
A_n-type AGT correspondence anticipates that conformal blocks of A_n Toda CFT are related to partition functions of a family of 4d N=2 SCFTs. We use gauge/vortex duality to both give a precise form of the correspondence, and to prove it.…
Conformal blocks and their AGT relations to LMNS integrals and Nekrasov functions are best described by "conformal" (or Dotsenko-Fateev) matrix models, but in non-Gaussian Dijkgraaf-Vafa phases, where different eigenvalues are integrated…
An elementary introduction to the 2d/4d correspondences is given. After quickly reviewing the 2d q-deformed Yang-Mills theory and the Liouville theory, we will introduce 4d theories obtained by coupling trifundamentals to SU(2) gauge…
Inspired by Polyakov's original formulation of quantum Liouville theory through functional integral, we analyze perturbation expansion around a classical solution. We show the validity of conformal Ward identities for puncture operators and…
The best way to represent generic conformal blocks is provided by the free-field formalism, where they acquire a form of multiple Dotsenko-Fateev-like integrals of the screening operators. Degenerate conformal blocks can be described by the…
This is the first part of an investigation concerning the formulation of 2D gravity in the framework of the uniformization theory of Riemann surfaces. As a first step in this direction we show that the classical Liouville action appears in…
We study the boundary correlation functions in Liouville theory and in solvable statistical models of 2D quantum gravity. In Liouville theory we derive functional identities for all fundamental boundary structure constants, similar to the…
We define a three-parameter family of random surfaces in Liouville quantum gravity (LQG) which can be viewed as the quantum version of triangles. These quantum triangles are natural in two senses. First, by our definition they produce the…
In the example of the Schr\"odinger/KdV equation we give elementary treatment of the theory of finite-gap integration. The concept is equivalent to two kinds of Liouvillian integrability: quadrature integrability of linear differential…