Related papers: Minimal lectures on two-dimensional conformal fiel…
We present analytical implementation of conformal field theory on a compact Riemann surface. We consider statistical fields constructed from background charge modifications of the Gaussian free field and derive Ward identities which…
These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on…
Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…
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…
Liouville conformal field theory is a prototypical example of an exactly solvable quantum field theory, in the sense that the correlation functions in an arbitrary background can be determined exactly using only the constraints of unitarity…
We construct crosscap states in the N = 2 Liouville theory from the modular bootstrap method. We verify our results by comparing it with the calculation from the minisuperspace approximation and by checking the consistency with the…
We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the…
Virasoro conformal blocks are universal ingredients of correlation functions of two-dimensional conformal field theories (2d CFTs) with Virasoro symmetry. It is acknowledged that in the (classical) limit of large central charge of the…
We investigate the limit of minimal model conformal field theories where the central charge approaches one. We conjecture that this limit is described by a non-rational CFT of central charge one. The limiting theory is different from the…
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…
We study conformal twist field four-point functions on a $\mathbb Z_N$ orbifold. We examine in detail the case $N=3$ and analyze theories obtained by replicated $N$-times a minimal model with central charge $c<1$. A fastly convergent…
A powerful approach to the celebrated Wess-Zumino-Witten (WZW) model is provided by its free-field realization. However, explicit calculations of conformal blocks are not described in the literature in full detail. We begin this study with…
Unlike conformal boundary conditions, conformal defects of Virasoro minimal models lack classification. Alternatively to the defect perturbation theory and the truncated conformal space approach, we employ open string field theory (OSFT)…
Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined…
In this article we prove smoothness of the correlation functions in probabilistic Liouville Conformal Field Theory. Our result is a step towards proving that the correlation functions satisfy the higher Ward identities and the higher BPZ…
We find non-rational conformal field theories in two dimensions, which are solvable due to their correlators being related to correlators of Liouville theory. Their symmetry algebra consists of the dimension-two stress-energy tensor, and…
The conformal bootstrap is applied to percolation and dilute self-avoiding polymers, two theories with Virasoro central charge $c=0$ in two dimensions. In both cases we propose a spectrum of operators motivated by Virasoro symmetry which is…
We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…
Conformal Carrollian groups are known to be isomorphic to Bondi-Metzner-Sachs (BMS) groups that arise as the asymptotic symmetries at the null boundary of Minkowski spacetime. The Carrollian algebra is obtained from the Poincare algebra by…
We give explicit field theoretical representations for the observables of 2+1 dimensional Chern-Simons theory in terms of gauge invariant composites of 2D WZW fields. To test our identification we compute some basic Wilson loop correlators…