Matthias R. Gaberdiel

A rational logarithmic conformal field theory

Abstract We analyse the fusion of representations of the triplet algebra, the maximally extended symmetry algebra of the Virasoro algebra at c = −2. It is shown that there exists a finite number of representations which are closed under fusion. These include all irreducible representations, but also some reducible representations which appear as indecomposable components in fusion products.

A Local logarithmic conformal field theory

The local logarithmic conformal field theory corresponding to the triplet algebra at c = -2 is constructed. The constraints of locality and duality are explored in detail, and a consistent set of amplitudes is found. The spectrum of the corresponding theory is determined, and it is found to be modular invariant. This provides the first construction of a non-chiral rational logarithmic conformal field theory, establishing that such models can indeed define bona fide conformal field theories.

Stable non-BPS D-particles

Abstract It is shown that the orbifold of type IIB string theory by (−1) F L I 4 admits a stable non-BPS Dirichlet particle that is stuck on the orbifold fixed plane. It is charged under the SO (2) gauge group coming from the twisted sector, and transforms as a long multiplet of the D =6 supersymmetry algebra. This suggests that it is the strong coupling dual of the perturbative stable non-BPS state that appears in the orientifold of type IIB by Ω I 4 .

Dualities of type 0 strings

It is conjectured that the two closed bosonic string theories, type 0A and type 0B, correspond to certain supersymmetry breaking orbifold compactifications of M-theory. Various implications of this conjecture are discussed, in particular the behaviour of the tachyon at strong coupling and the existence of non-perturbative fermionic states in type 0A. The latter are shown to correspond to bound states of type 0A D-particles, thus providing further evidence for the conjecture. We also give a comprehensive description of the various type 0 closed and open string theories.

Lectures on non-BPS Dirichlet branes

A comprehensive introduction to the boundary state approach to Dirichlet branes is given. Various examples of BPS and non-BPS Dirichlet branes are discussed. In particular, the non-BPS states in the duality of Type IIA on K3 and the heterotic string on T 4 are analysed in detail.

The no-ghost theorem for AdS3 and the stringy exclusion principle

A complete proof of the no-ghost theorem for bosonic and fermionic string theories on AdS3, or the group manifold of SU(1, 1), is given. It is then shown that the restriction on the spin (in terms of the level) that is necessary to obtain a ghost-free spectrum corresponds to the stringy exclusion principle of Maldacena and Strominger.

Open string-string junction transitions

Abstract It is confirmed that geodesic string junctions are necessary to describe the gauge vectors of symmetry groups that arise in the context of 1113 superstrings compactified in the presence of nonlocal 7-branes. By examining the moduli space of 7-brane backgrounds for which the dilaton and axion fields are constant, we are able to describe explicitly and geometrically how open string geodesics can fail to be smooth, and how geodesic string junctions then become the relevant BPS representatives of the gauge bosons. The mechanisms that guarantee the existence and uniqueness of the BPS representative of any gauge vector are also shown to generalize to the case where the dilaton and axion fields are not constant.

Matrix factorisations and permutation branes

The description of B-type D-branes on a tensor product of two N = 2 minimal models in terms of matrix factorisations is related to the boundary state description in conformal field theory. As an application we show that the D0- and D2-brane for a number of Gepner models are described by permutation boundary states. In some cases (including the quintic) the images of the D2-brane under the Gepner monodromy generate the full charge lattice.

An introduction to conformal field theory

A comprehensive introduction to two-dimensional conformal field theory is given. The structure of the meromorphic subtheory is described in detail, and a number of examples are presented explicitly. Standard constructions such as the coset and the orbifold construction are explained. The concept of a representation of the meromorphic theory is introduced, and the role of Zhus algebra in classifying highest weight representations is elucidated. The fusion product of two representations and the corresponding fusion rules are defined, and Verlindes formula is explained. Finally, higher correlation functions are considered, and the polynomial relations of Moore and Seiberg and the quantum group structure of chiral conformal field theory are discussed. The treatment is relatively general and also allows for a description of less well known classes of theories such as logarithmic conformal field theories.

Rationality, quasirationality and finite W-algebras

Abstract:u2002Some of the consequences that follow from the C2 condition of Zhu are analysed. In particular it is shown that every conformal field theory satisfying the C2 condition has only finitely many n-point functions, and this result is used to prove a version of a conjecture of Nahm, namely that every representation of such a conformal field theory is quasirational. We also show that every such vertex operator algebra is a finite W-algebra, and we give a direct proof of the convergence of its characters as well as the finiteness of the fusion rules.