`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

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

On the String Actions for the Generalized Two-dimensional Yang-Mills Theories

We study the structures of partition functions of the large $N$ generalized two-dimensional Yang-Mills theories ($gYM_2$) by recasting the higher Casimirs. We clarify the appropriate interpretations of them and try to extend the Cordes-Moore-Ramgoolam's topological string model describing the ordinary $YM_2$ \cite{CMR} to those describing $gYM_2$. We present the expressions of the appropriate operators to reproduce the higher Casimir terms in $gYM_2$. The concept of ''deformed gravitational descendants'' will be introduced for this purpose.Comment: 12 pages, no figures, version to be published in Mod.Phys.Lett.

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

Boundary States of D-branes in AdS_3 Based on Discrete Series

We study D-branes in the Lorentzian AdS_3 background from the viewpoint of boundary states, emphasizing the role of open-closed duality in string theory. Employing the world sheet with Lorentzian signature, we construct the Cardy states with the discrete series. We show that they are compatible with (1) unitarity and normalizability, and (2) the spectral flow symmetry, in the open string spectrum. We also discuss their brane interpretation. We further show that in the case of superstrings on AdS_3 x S^3 x T^4, our Cardy states yield an infinite number of physical BPS states in the open string channel, on which the spectral flows act consistently.Comment: 27 pages, latex, no figures, v2: we discuss on the single cover of AdS_3 rather than the universal cover, reference added, v3: Appendix B and reference adde

Non-BPS Fractional Branes with Bose-Fermi Cancellation in Asymmetric Orbifolds

We study non-BPS D-branes in the type II string vacua with chiral space-time SUSY constructed based on the asymmetric orbifolds of \mbox{K3} \cong T^4/{\Bbb Z}_2 as a succeeding work of arXiv:1704.05262[hep-th]. We especially focus on the fractional D-branes that contains the contributions from the twisted sector of the ${\Bbb Z}_2$ orbifolding. We show that the cylinder partition functions for these fractional branes do not vanish, as in the cases of ordinary non-BPS D-branes. This aspect is in a sharp contrast with the bulk-type branes studied in arXiv:1704.05262[hep-th]. We then discuss the extensions of models by including the discrete torsion depending on the spin structures, and investigate whether we obtain the vanishing self-overlaps associated to the fractional branes. The existence/absence of bose-fermi cancellations both in the closed and open string spectra as well as the massless spectra in the twisted sectors crucially depend on the discrete torsion. We find that some choices of the torsion indeed realize the vanishing self-overlaps for the fractional branes, with keeping the vanishing torus partition function intact.Comment: 1+30 pages, no figur

Fractional Strings in (p,q) 5-brane and Quiver Matrix String Theory

We study the (p,q)5-brane dynamics from the viewpoint of Matrix string theory in the T-dualized ALE background. The most remarkable feature in the (p,q)5-brane is the existence of ``fractional string'', which appears as the instanton of 5-brane gauge theory. We approach to the physical aspects of fractional string by means of the two types of Matrix string probes: One of which is that given in hep-th/9710065. As the second probe we present the Matrix string theory describing the fractional string itself. We calculate the moduli space metrics in the respective cases and argue on the specific behaviors of fractional string. Especially, we show that the ``joining'' process of fractional strings can be realized as the transition from the Coulomb branch to the Higgs branch of the fractional string probe. In this argument, we emphasize the importance of some monodromies related with the theta-angle of the 5-brane gauge theory.Comment: 21 pages, Late