(Super-) String in Two Dimensional Black Hole and Target Space Dualities

We review the recently proposed string theory in two dimensional black hole background. Especially, the structure of the duality in the target space is discussed. The duality is analogous to \lq\lq $R \rightarrow 1/R$" symmetry of a compactified boson. We consider the duality in more general target space manifolds which have Killing symmetries and we give an explicit formula which connects two different manifolds which are dual to each other. Superstring theory in two dimensional black hole background is also discussed based on supersymmetric $SU(1,1)/U(1)$ gauged Wess-Zumino-Witten model.Comment: 19pp (Talk at YITP workshop, ``Developments in Strings and Field Theories'', Kyoto, JAPAN

Group Theoretical Structure of N=1N=1 and N=2N=2 Two-Form Supegravity

We clarifies the group theoretical structure of $N=1$ and $N=2$ two-form supergravity, which is classically equivalent to the Einstein supergravity. $N=1$ and $N=2$ two-form supergravity theories can be formulated as gauge theories. By introducing two Grassmann variables $\theta^A$ ($A=1,2$), we construct the explicit representations of the generators $Q^i$ of the gauge group, which makes to express any product of the generators as a linear combination of the generators $Q^iQ^j=\sum_k f^{ij}_k Q^k$. By using the expression and the tensor product representation, we explain how to construct finite-dimensional representations of the gauge groups. Based on these representations, we construct the Lagrangeans of $N=1$ and $N=2$ two-form supergravity theories.Comment: Latex file, 15

Inverse problem - reconstruction of dark energy models

We review how we can construct the gravity models which reproduces the arbitrary development of the universe. We consider the reconstruction in the Einstein gravity coupled with generalized perfect fluid, scalar-Einstein gravity, scalar-Einstein-Gauss-Bonnet gravity, Einstein-$F(G)$-gravity, and $F(R)$-gravity. Very explicit formulas are given to reconstruct the models, which could be used when we find the detailed data of the development of the universe by future observations. Especially we find the formulas using e-foldings, which has a direct relation with observed redshift. As long as we observe the time development of the Hubble rate $H$, there exists a variety of models describing the arbitrary development of universe.Comment: LaTeX 11 pages, references are added, to appear in Proceedings of International Workshop on Dark Matter, Dark Energy and Matter-Antimatter Asymmetry, National Tsing Hua University, Hsinchu, Taiwan, November 20-21, 200

Exact Four Dimensional Exploding Universe Solution in String Theory

We obtain a four dimensional exploding universe solution in string theory. The solution is obtained from the string theory in the flat background by using non-abelian $T$-duality and the analytic continuation. In the solution, the radius of the universe is finite for fixed time and the universe is surrounded with the boundary which is composed of the singularity. The boundary runs away with the speed of light and the flat space-time is left behind.Comment: Latex file, 6 pages, misprints in Eqs.(14), (16), (19) and (26) are correcte

Wormholes in Two Dimensional Dilaton Gravity

It is shown that the general solution of classical equations of motion in two dimensional dilaton gravity proposed by Callan, Giddings, Harvey and Strominger (CGHS) includes a Lorentzian wormhole solution in addition to a black hole solution. We also show that matter perturbation of the wormhole by a shock wave leads to the formation of a black hole where the curvature singularity is cloaked by the global event horizon. It is also argued that the classical wormhole would be stable against quantum corrections.Comment: INS-Rep.-1012, NDA-FP-13/93, OCHA-PP-37, LATEX file, 9p