Fusion of twisted representations

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and determine the analogue of Zhu's algebra for arbitrary twisted representations. As an example we study the fusion of representations of the Ramond sector of the N=1 and N=2 superconformal algebra. In the latter case, certain subtleties arise which we describe in detail.Comment: 24 pages, LATE

An explicit construction of the quantum group in chiral WZW-models

It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of representations of the chiral algebra and finite dimensional internal parameter spaces. On this enlarged space there exists a natural action of Drinfeld's quasi quantum group $A_{g,t}$, which commutes with the action of the chiral algebra and plays the r\^{o}le of an internal symmetry algebra. The $R$ matrix describes the braiding of the chiral vertex operators and the coassociator $\Phi$ gives rise to a modification of the duality property. For generic $q$ the quasi quantum group is isomorphic to the coassociative quantum group $U_{q}(g)$ and thus the duality property of the chiral theory can be restored. This construction has to be modified for the physically relevant case of integer level. The quantum group has to be replaced by the corresponding truncated quasi quantum group, which is not coassociative because of the truncation. This exhibits the truncated quantum group as the internal symmetry algebra of the chiral WZW model, which therefore has only a modified duality property. The case of $g=su(2)$ is worked out in detail.Comment: 28 pages, LATEX; a remark about other possible symmetry algebras and some references are adde

Stable non-BPS D-particles

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 \Omega I_4.Comment: 10 pages, LaTe

Non-BPS States in Heterotic - Type IIA Duality

The relation between some perturbative non-BPS states of the heterotic theory on T^4 and non-perturbative non-BPS states of the orbifold limit of type IIA on K3 is exhibited. The relevant states include a non-BPS D-string, and a non-BPS bound state of BPS D-particles (`D-molecule'). The domains of stability of these states in the two theories are determined and compared.Comment: 17 pages LaTex, 1 figure; Minor correction in subsection 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.Comment: 23 pages LaTex, 1 figure. Error corrected in table 1. Version to appear in JHE

Triality in Minimal Model Holography

The non-linear W_{\infty}[\mu] symmetry algebra underlies the duality between the W_N minimal model CFTs and the hs[\mu] higher spin theory on AdS_3. It is shown how the structure of this symmetry algebra at the quantum level, i.e. for finite central charge, can be determined completely. The resulting algebra exhibits an exact equivalence (a`triality') between three (generically) distinct values of the parameter \mu. This explains, among other things, the agreement of symmetries between the W_N minimal models and the bulk higher spin theory. We also study the consequences of this triality for some of the simplest W_{\infty}[\mu] representations, thereby clarifying the analytic continuation between the`light states' of the minimal models and conical defect solutions in the bulk. These considerations also lead us to propose that one of the two scalar fields in the bulk actually has a non-perturbative origin.Comment: 29 pages; v2. Typos correcte

Twisted brane charges for non-simply connected groups

The charges of the twisted branes for strings on the group manifold SU(n)/Z_d are determined. To this end we derive explicit (and remarkably simple) formulae for the relevant NIM-rep coefficients. The charge groups of the twisted and untwisted branes are compared and found to agree for the cases we consider.Comment: 30 page