Related papers: Modular bootstrap in Liouville field theory
We present a rigorous proof of the Dorn, Otto, Zamolodchikov, Zamolodchikov formula (the DOZZ formula) for the 3 point structure constants of Liouville Conformal Field Theory (LCFT) starting from a rigorous probabilistic construction of the…
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…
A recent claim that the S-duality between 4d SUSY gauge theories, which is AGT related to the modular transformations of 2d conformal blocks, is no more than an ordinary Fourier transform at the perturbative level, is further traced down to…
We study the conformal field theory dual of the type IIA flux compactification model of DeWolfe, Giryavets, Kachru and Taylor, with all moduli stabilized. We find its central charge and properties of its operator spectrum. We concentrate on…
The well known Liouville-Arnold theorem says that if a level surface of integrals of an integrable system is compact and connected, then it is a torus. However, in some important examples of integrable systems the topology of a level…
Liouville Conformal Field Theory (LCFT) on the disk describes the conformal factor of the quantum disk, which is the natural random surface in Liouville quantum gravity with disk topology. Fateev, Zamolodchikov and Zamolodchikov (2000)…
We consider the two-dimensional $\mathfrak{sl}_n$ quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry ($W_n$ algebra), a central charge $c \leq n-1$ and a continuous…
Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
By choosing an unconventional polarization of the connection phase space in (2+1)-gravity on the torus, a modular invariant quantum theory is constructed. Unitary equivalence to the ADM-quantization is shown.
We propose an exact formula for three-point functions on the sphere in critical loop models with primary fields $V_{(r,s)}$ characterized by $2r$ legs and a parameter \(s\) that describes diagonal fields for $r=0$ and the momentum of legs…
The tau function on the moduli space of generic holomorphic 1-differentials on complex algebraic curves is interpreted as a section of a line bundle on the projectivized Hodge bundle over the moduli space of stable curves. The asymptotics…
We revisit ADE minimal string theories, focusing on the D- and E-series minimal models coupled to Liouville theory. Unlike the A-series, whose duals are solvable two-matrix models, these theories are conjectured to correspond to unsolvable…
This paper is the first part of the proof of the conformal bootstrap for Liouville conformal field theory on surfaces with a boundary, devoted to Segal's axioms in this context. We introduce the notion of Segal's amplitudes on surfaces with…
In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus…
The quantum theory of the Liouville model with imaginary field is considered using the quantum inverse scattering method. An integrable structure with nontrivial spectral parameter dependence is developed for lattice Liouville theory by…
We study conformal boundary conditions and corresponding one-point functions of the N=2 super-Liouville theory using both conformal and modular bootstrap methods. We have found both continuous (`FZZT-branes') and discrete (`ZZ-branes')…
The partition function of a family of four dimensional N=2 gauge theories has been recently related to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory…
We study the Virasoro conformal block decomposition of the genus two partition function of a two-dimensional CFT by expanding around a Z3-invariant Riemann surface that is a three-fold cover of the Riemann sphere branched at four points,…
We show that any 2D scalar field theory compactified on a cylinder and with a Fourier expandable potential $V$ is equivalent, in the small coupling limit, to a 1D theory involving a massless particle in a potential $V$ and an infinite tower…