We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kähler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the...

The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant under conformal transformations. They define conformal field theories satisfying equations of the biharmonic type. Two kinds of these biharmonic field theorie...

The periods of arbitrary abelian forms on hyperelliptic Riemann surfaces, in particular the periods of the meromorphic Seiberg-Witten differential λ SW , are shown to be in one-to-one correspondence with the conformal blocks of correlation functions of the rational logarithmic conformal field theory with central charge c = c 2,1 = −2. The fields of this theory precisely simulate the branched do...

We analyse the SU(2) k WZNW models beyond the integrable representations and in particular the case of SU(2) 0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally produced in the fusion of discrete irreducible representations. We also find extra, chiral and non-chiral, multiplet structure in the theory. The chiral fields,...

We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two– and three– point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ord...

Representations of the superalgebra osp(2|2) and current superalgebra osp(2|2) (1) k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2|2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2|2) (1) k in the standard basis are obtained for arbitrary level k.

The string theory is a fast moving subject, both physics wise and in the respect of mathematics. In order to keep up with the discipline it is important to move with new ideas which are being stressed. Here I wish to give extracts from new papers of ideas which I have recently found interesting. There are six papers which are involved: I ."Strings formulated directly in 4 dimensions " A. N...

Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of CFT appear in a more straightforward manner; and because it has important applications: in string theory in the physics of open strings and D-branes, and in ...