Non-geometric Backgrounds Based on Topological Interfaces

We study simple models of the world-sheet CFTs describing non-geometric backgrounds based on the topological interfaces, the `gluing condition' of which imposes T-duality- or analogous twists. To be more specific, we start with the torus partition function on a target space S^1 [base] x (S^1 x S^1) [fiber] with rather general values of radii. The fiber CFT is defined by inserting the twist operators consisting of the topological interfaces which lie along the cycles of the world-sheet torus according to the winding numbers of the base circle. We construct the partition functions involving such duality twists. The modular invariance is achieved straightforwardly, whereas `unitarization' is generically necessary to maintain the unitarity. We demonstrate it in the case of the equal fiber radii. The resultant models are closely related to the CFTs with the discrete torsion. The unitarization is also physically interpreted as multiple insertions of the twist/interface operators along various directions.Comment: 32 pages, no figures; (v2) comments and explanations adde

Non-supersymmetric D-branes with Vanishing Cylinder Amplitudes in Asymmetric Orbifolds

We study the type II string vacua with chiral space-time SUSY constructed as asymmetric orbifolds of torus and $K3$ compactifications. Despite the fact that all the D-branes are non-BPS in any chiral SUSY vacua, we show that the relevant non-geometric vacua of asymmetric orbifolds allow rather generally configurations of D-branes which lead to vanishing cylinder amplitudes, implying the bose-fermi cancellation at each mass level of the open string spectrum. After working on simple models of toroidal asymmetric orbifolds, we focus on the asymmetric orbifolds of $T^2 \times {\cal M}$, where ${\cal M}$ is described by a general ${\cal N} =4$ SCFT with $c=6$ defined by the Gepner construction for $K3$. Even when the modular invariant partition functions in the bulk remain unchanged, the spectra of such non-BPS D-branes with the bose-fermi cancellation can vary significantly according to the choice of orbifolding.Comment: 32 pages, no figures; (v2) comments and discussion added on properties of D-brane

`Analytic Continuation' of N=2 Minimal Model

In this paper we discuss what theory should be identified as the `analytic continuation' with $N \rightarrow -N$ of the ${\cal N}=2$ minimal model with the central charge $\hat{c} = 1 - \frac{2}{N}$. We clarify how the elliptic genus of the expected model is written in terms of {\em holomorphic\/} linear combinations of the `modular completions' introduced in [arXiv:1012.5721 [hep-th]] in the $SL(2)_{N+2}/U(1)$-supercoset theory. We further discuss how this model could be interpreted as a kind of {\em `compactified'} model of the $SL(2)_{N+2}/U(1)$-supercoset in the $(\tilde{R},\tilde{R})$-sector, in which only the discrete spectrum appears in the torus partition function and the potential IR-divergence due to the non-compactness of target space is removed. We also briefly argue on possible definitions of the sectors with other spin structures.Comment: 1+29 pages, no figur