Open string T-duality in double space

The role of double space is essential in new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of open string is missing in such approach because until now there have been no appropriate formulation of open string T-duality. In the previous paper [1], we showed how to introduce vector gauge fields $A^N_a$ and $A^D_i$ at the end-points of open string in order to enable open string invariance under local gauge transformations of the Kalb-Ramond field and its T-dual "restricted general coordinate transformations". We demonstrated that gauge fields $A^N_a$ and $A^D_i$ are T-dual to each other. In the present article we prove that all above results can be interpreted as coordinate permutations in double space.Comment: 18 page

Dilaton field induces commutative Dp-brane coordinate

It is well known that space-time coordinates and corresponding Dp-brane world-volume become non-commutative, if open string ends on Dp-brane with Neveu-Schwarz background field $B_{\mu \nu}$. In this paper we extend these considerations including the dilaton field $\Phi$, linear in coordinates $x^\mu$. In that case the conformal part of the world-sheet metric appears as new non-commutative variable and the coordinate in direction orthogonal to the hyper plane $\Phi = const$, becomes commutative.Comment: Latex, 14 pages, Added reference and improve conten

Canonical approach to 2D induced gravity

Using canonical method the Liouville theory has been obtained as a gravitational Wess-Zumino action of the Polyakov string. From this approach it is clear that the form of the Liouville action is the consequence of the bosonic representation of the Virasoro algebra, and that the coefficient in front of the action is proportional to the central charge and measures the quantum braking of the classical symmetry.Comment: RevTeX, 19 page

Gauge symmetries decrease the number of Dp-brane dimensions

It is known that the presence of antisymmetric background field $B_{\mu\nu}$ leads to noncommutativity of Dp-brane manifold. Addition of the linear dilaton field in the form $\Phi(x)=\Phi_0+a_\mu x^\mu$, causes the appearance of the commutative Dp-brane coordinate $x=a_\mu x^\mu$. In the present article we show that for some particular choices of the background fields, $a^2\equiv G^{\mu\nu}a_\mu a_\nu=0$ and $\tilde a^2\equiv [ (G-4BG^{-1}B)^{-1}\ ]^{\mu\nu}a_\mu a_\nu=0$, the local gauge symmetries appear in the theory. They turn some Neuman boundary conditions into the Dirichlet ones, and consequently decrease the number of the Dp-brane dimensions.Comment: We improve Sec.4. and Conclusion and we added the Appendix in order to clarify result

CT-duality as a local property of the world-sheet

In the present article, we study the local features of the world-sheet in the case when probe bosonic string moves in antisymmetric background field. We generalize the geometry of surfaces embedded in space-time to the case when the torsion is present. We define the mean extrinsic curvature for spaces with Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, the field equation is just the equality of mean extrinsic curvature and extrinsic mean torsion, which we call CT-duality. To the world-sheet described by this relation we will refer as CT-dual surface.Comment: Latex, 15 pages, 2 Figure

Type I background fields in terms of type IIB ones

We choose such boundary conditions for open IIB superstring theory which preserve N=1 SUSY. The explicite solution of the boundary conditions yields effective theory which is symmetric under world-sheet parity transformation $\Omega:\sigma\to-\sigma$. We recognize effective theory as closed type I superstring theory. Its background fields,beside known $\Omega$ even fields of the initial IIB theory, contain improvements quadratic in $\Omega$ odd ones.Comment: 4 revtex pages, no figure

Nongeometric background arising in the solution of Neumann boundary conditions

We investigate the open string propagation in the weakly curved background with the Kalb-Ramond field containing an infinitesimal part, linear in coordinate. Solving the Neumann boundary conditions, we find the expression for the space-time coordinates in terms of the effective ones. So, the initial theory reduces to the effective one. This effective theory is defined on the nongeometric doubled space $(q^\mu,\tilde{q}_\mu)$, where $q^\mu$ is the effective coordinate and $\tilde{q}_\mu$ is its T-dual. The effective metric depends on the coordinate $q^\mu$ and there exists non-trivial effective Kalb-Ramond field which depends on the T-dual coordinate $\tilde{q}_\mu$. The fact that $\tilde{q}_\mu$ is $\Omega$-odd leads to the nonvanishing effective Kalb-Ramond field