Related papers: Probabilistic interpretation of quantum field theo…
As an existence proof of the (0,2) heterotic supercurrent supermultiplets in (1+1) dimensional quantum field theories which are consistent with the warped superconformal algebra, we construct the (0,2) chiral Liouville field theories. The…
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…
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…
The Liouville action emerges as the effective action of 2-d gravity in the process of path integral quantization of the bosonic string. It yields a measure of the violation of classical symmetries of the theory at the quantum level. Certain…
The conformal symmetry in the Liouville theory is analysed by using the Hamiltonian light--front formalism. The boundary conditions of dynamical variables are seen to involve an arbitrary function of time, so that the standard methods for…
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…
The quantum discrete Liouville model in the strongly coupled regime, 1<c<25, is formulated as a well defined quantum mechanical problem with unitary evolution operator. The theory is self-dual: there are two exponential fields related by…
We construct a mathematical version of quantum field theory. It assigns to a multidimensional variational principle an associative algebra which is a quantization of the Poisson algebra of classical field theory observables. For free scalar…
(This talk was presented at the Third International Wigner Symposium on Group Theory, Oxford, September, 1993.) Matrix models provides us with the most powerful framework in which to analyze D=2 string theory, yet some of its miraculous…
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…
Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of a log-correlated real scalar field with a background charge and an exponential potential. We analyse the LCFT on a four-dimensional manifold with a boundary.…
The continuation of the Liouville conformal field theory to c<=1 is considered. The viability of an interpretation involving a timelike boson which is the conformal factor for two-dimensional asymptotically de Sitter geometries is examined.…
This is the 11th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. It describes an approach to understanding the 4d/2d relations discovered by Alday, Gaiotto and Tachikawa by…
I review a particular class of physical applications of Logarithmic Conformal Field Theory in strings propagating in changing (not necessarily conformal) backgrounds, namely D-brane recoil in flat or time-dependent cosmological backgrounds.…
I review recent results on conformal field theories in four dimensions and quantum field theories interpolating between conformal fixed points, supersymmetric and non-supersymmetric. The talk is structured in three parts: i) central…
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in…
Superconformal field theory with $\mathcal{N}=2$ supersymmetry in four dimensional spacetime provides a prime playground to study strongly coupled phenomena in quantum field theory. Its rigid structure ensures valuable analytic control over…
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…
In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new…