We first discuss the relationship between the SL(2; R)/U (1) supercoset and N = 2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2; R)/U (1) theory correspond exactly to those massless representations of N = 2 Liouville theory which are closed under modular transformations and studied in our previous work [18].It is known that toroidal partition functions of SL(2; R)/U (1) theory (2D Black Hole) contain two parts, continuous and discrete representations. The contribution of continuous representations is proportional to the space-time volume and is divergent in the infinitevolume limit while the part of discrete representations is volume-independent.In order to see clearly the contribution of discrete representations we consider elliptic genus which projects out the contributions of continuous representations: making use of the SL(2; R)/U (1), we compute elliptic genera for various non-compact space-times such as the conifold, ALE spaces, Calabi-Yau 3-folds with A n singularities etc. We find that these elliptic genera in general have a complex modular property and are not Jacobi forms as opposed to the cases of compact Calabi-Yau manifolds.

Aicardi-Goutières syndrome (AGS) is a rare, genetically determined early-onset progressive encephalopathy. To date, mutations in six genes have been identified as etiologic for AGS. Our Japanese nationwide AGS survey identified six AGS-affected individuals without a molecular diagnosis; we performed whole-exome sequencing on three of these individuals. After removal of the common polymorphisms found in SNP databases, we were able to identify IFIH1 heterozygous missense mutations in all three. In vitro functional analysis revealed that IFIH1 mutations increased type I interferon production, and the transcription of interferon-stimulated genes were elevated. IFIH1 encodes MDA5, and mutant MDA5 lacked ligand-specific responsiveness, similarly to the dominant Ifih1 mutation responsible for the SLE mouse model that results in type I interferon overproduction. This study suggests that the IFIH1 mutations are responsible for the AGS phenotype due to an excessive production of type I interferon.

In this paper we construct the time dependent boundary states describing the "rolling D-brane solutions" in the NS5 background discovered recently by Kutasov by means of the classical DBI analysis. We first survey some aspects of non-compact branes in the NS5 background based on known boundary states in the N = 2 Liouville theory. We consider two types of non-compact branes, one of which is BPS and the other is non-BPS but stable. Then we clarify how to Wick-rotate the non-BPS one appropriately. We show that the Wick-rotated boundary state realizes the correct trajectory of rolling D-brane in the classical limit, and leads to well behaved spectral densities of open strings due to the existence of non-trivial damping factors of energy. We further study the cylinder amplitudes and the emission rates of massive closed string modes.

We present our recent studies on the dynamics of boundary N = 2 Liouville theory. We use the representation theory of N = 2 superconformal algebra and the method of modular bootstrap to derive three classes of boundary states of the N = 2 Liouville theory. Class 1 and 2 branes are analogues of ZZ and FZZT branes of N = 0, 1 Liouville theory while class 3 branes come from U(1) degrees of freedom. We compare our results with those of SL(2; R)/U (1) super-coset which is known to be T-dual to N = 2 Liouville theory and describes the geometry of 2d black hole. We find good agreements with known results in SL(2; R)/U (1) theory obtained by semi-classical analysis using DBI action. We also comment on the duality of N = 2 Liouville theory.