Related papers: Structure constants for the osp(1|2) current algeb…
We construct a large class of conformal interfaces between two-dimensional c=1 conformal field theories describing compact free bosons and their Z_2 orbifolds. The interfaces are obtained by constructing boundary states in the corresponding…
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…
We study conformal field theory with the symmetry algebra $\mathcal{A}(2,p)=\hat{\mathfrak{gl}}(n)_{2}/\hat{\mathfrak{gl}}(n-p)_2$. In order to support the conjecture that this algebra acts on the moduli space of instantons on…
We construct two-dimensional conformal field theories with a Z_N symmetry, based on the second solution of Fateev-Zamolodchikov for the parafermionic chiral algebra. Primary operators are classified according to their transformation…
The conformal field theory for the $gl(N,N)$ affine Lie superalgebra in two space-time dimensions is studied. The energy-momentum tensor of the model, with vanishing Virasoro anomaly, is constructed. This theory has a topological symmetry…
In this paper we study a family of commutative algebras generated by two infinite sets of generators. These algebras are parametrized by Young diagrams. We explain a connection of these algebras with the fusion product of integrable…
We examine the dynamics of a free massless scalar field on a figure eight network. Upon requiring the scalar field to have a well defined value at the junction of the network, it is seen that the conserved currents of the theory satisfy…
Parafermionic conformal field theories are considered on a purely algebraic basis. The generalized Jacobi type identity is presented. Systems of free fermions coupled to each other by nontrivial parafermionic type relations are studied in…
A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic symmetry is used to construct four-point N=1 super Liouville conformal block, which…
The two-point functions in affine current algebras based on simple Lie algebras are constructed for all representations, integrable or non-integrable. The weight of the conjugate field to a primary field of arbitrary weight is immediately…
Using explicit results for the four-point correlation functions of the Wess-Zumino-Novikov-Witten (WZNW) model we discuss the conformal embedding osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0). This embedding has emerged in Bernard and LeClair's…
We construct boundary states in a particular c=1 conformal field theory, the SU(2)_1/G orbifold with G a binary finite subgroup of SU(2). These states preserve the conformal symmetry, at least, but break rational symmetries of the SU(2)_1/G…
It has long been clear that the conformal bootstrap is associated with a rich geometry. In this paper we undertake a systematic exploration of this geometric structure as an object of study in its own right. We study conformal blocks for…
We study a three dimensional conformal field theory in terms of its partition function on arbitrary curved spaces. The large $N$ limit of the nonlinear sigma model at the non-trivial fixed point is shown to be an example of a conformal…
The Polyakov's "soldering procedure" which shows how two-dimensional diffeomorphisms can be obtained from SL(2,R) gauge transformations is discussed using the free-field representation of SL(2,R) current algebra. Using this formalism, the…
We analyze the free energy of the integrable two dimensional O(4) sigma model in a magnetic field. We use Volin's method to extract high number (2000) of perturbative coefficients with very high precision. The factorial growth of these…
The d=10 type II string theories, d=11 M-theory and d=12 F-theory have the same symmetry group. It can be viewed either as a subgroup of a conformal group OSp(1|64) or as a contraction of OSp(1|32). The theories are related by different…
We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.
We find a simple relation between two-dimensional BPS N=2 superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2,2) superconformal theories…
The minimal model $\mathfrak{osp}(1|2)$ vertex operator superalgebras are the simple quotients of affine vertex operator superalgebras constructed from the affine Lie super algebra $\widehat{\mathfrak{osp}}(1|2)$ at certain rational values…