Related papers: Modular bootstrap in Liouville field theory
We calculate numerically the torus one-point string diagram in the two-dimensional string cosmology background by decomposing the one-point functions in $c=1$ and $c=25$ Liouville CFT into torus one-point Virasoro conformal blocks and…
The gauge formulation of Einstein gravity in AdS$_3$ background leads to a boundary theory that breaks modular symmetry and loses the covariant form. We examine the Weyl anomaly for the cylinder and torus manifolds. The divergent term is…
Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the…
To an RCFT corresponds two combinatorial structures: the amplitude of a torus (the 1-loop partition function of a closed string, sometimes called a modular invariant), and a representation of the fusion ring (called a NIM-rep or…
The Liouville field theory on Z_N-Riemann surfaces is studied and it is shown that it decomposes into a Liouville field theory on the sphere and N-1 free boson theories. Also, the partition function of the Liouville field theory on the…
An explicit construction for the monodromy of the Liouville conformal blocks in terms of Racah-Wigner coefficients of the quantum group U_q(sl(2,R)) is proposed. As a consequence, crossing-symmetry for four point functions is analytically…
We report novel analytic results for the Virasoro modular and fusion kernels relevant to 2d conformal field theories (CFTs), 3d topological field theories (TQFTs), and the representation theory of certain quantum groups. For all rational…
In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…
We try to develop a coherent picture on Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we…
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…
As regular conformal blocks describe the N=2 superconformal gauge theories in four dimensions, irregular conformal blocks are expected to reproduce the instanton partition functions of the Argyres-Douglas theories. In this paper, we…
The pentagram map is a discrete dynamical system defined on the moduli space of polygons in the projective plane. This map has recently attracted a considerable interest, mostly because its connection to a number of different domains, such…
We define the periodic Full Kostant-Toda on every simple Lie algebra, and show its Liouville integrability. More precisely we show that this lattice is given by a Hamiltonian vector field, associated to a Poisson bracket which results from…
We apply the factorization and vector bundle propositionerty of the sheaves of conformal blocks on $\overline{\mathscr{M}}_{g,n}$. defined by vertex operator algebras (VOAs) and give geometric proofs of essential results in the…
We study four-point correlation functions with logarithmic behaviour in Liouville field theory on a sphere, which consist of one kind of the local operators. We study them as non-integrated correlation functions of the gravitational sector…
It is shown that in the two-exponential version of Liouville theory the coefficients of the three-point functions of vertex operators can be determined uniquely using the translational invariance of the path integral measure and the…
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…
We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type…
We argue that the celestial conformal field theory exhibits patterns of a logarithmic conformal field theory. We uncover a Jordan block structure involving the celestial stress tensor and its logarithmic partner, a composite operator built…
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.…