Interaction of D-string with F-string: A Path-Integral Formalism

A path integral formalism is developed to study the interaction of an arbitrary curved Dirichlet (D-) string with elementary excitations of the fundumental (F-) string in bosonic string theory. Up to the next to leading order in the derivative expansion, we construct the properly renormalized vertex operator, which generalizes the one previously obtained for a D-particle moving along a curved trajectory. Using this vertex, an attempt is further made to quantize the D-string coordinates and to compute the quantum amplitude for scattering between elementary excitations of the D- and F-strings. By studying the dependence on the Liouville mode for the D-string, it is found that the vertex in our approximation consists of an infinite tower of local vertex operators which are conformally invariant on their respective mass-shell. This analysis indicates that, unlike the D-particle case, an off-shell extension of the interaction vertex would be necessary to compute the full amplitude and that the realization of symmetry can be quite non-trivial when the dual extended objects are simultaneously present. Possible future directions are suggested.Comment: 23 pages, latex, no figure

Generalized symmetries and invariant matter couplings in two-dimensional dilaton gravity

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area preserving transformations only contribute to the dynamics of the dilaton-gravity sector with a reshaping of the dilaton potential. The interaction with matter by means of invariant metrics is also considered. We show in a constructive way that there are metrics which are invariant under two of the symmetries. The most general metrics and minimal couplings that fulfil this condition are found.Comment: LateX file, no macros, 14pp: minor changes have been made and some misprints have been correcte

A Unified Approach to Solvable Models of Dilaton Gravity in Two-Dimensions Based on Symmetry

A large class of solvable models of dilaton gravity in two space-time dimensions, capable of describing black hole geometry, are analyzed in a unified way as non-linear sigma models possessing a special symmetry. This symmetry, which can be neatly formulated in the target-space-covariant manner, allows one to decompose the non-linearly interacting dilaton-gravity system into a free field and a field satisfying the Liouville equation with in general non-vanishing cosmological term. In this formulation, all the existent models are shown to fall into the category with vanishing cosmological constant. General analysis of the space-time structureinduced by a matter shock wave is performed and new models, with and without the cosmological term, are discussed.Comment: 29 pages, LaTe

Conformal and Nonconformal Symmetries in 2d Dilaton gravity

We study finite-dimensional extra symmetries of generic 2D dilaton gravity models. Using a non-linear sigma model formulation we show that the unique theories admitting an extra (conformal) symmetry are the models with an exponential potential $V \propto e^{\beta\phi}$ ($S ={1\over2\pi} \int d^2 x \sqrt{-g} [ R \phi + 4 \lambda^2 e^{\beta\phi} ]$), which include the CGHS model as a particular though limiting ($\beta=0$) case. These models give rise to black hole solutions with a mass-dependent temperature. The underlying extra symmetry can be maintained in a natural way in the one-loop effective action, thus implying the exact solubility of the semiclassical theory including back-reaction. Moreover, we also introduce three different classes of (non-conformal) transformations which are extra symmetries for generic 2D dilaton gravity models. Special linear combinations of these transformations turn out to be the (conformal) symmetries of the CGHS and $V \propto e^{\beta\phi}$ models. We show that one of the non-conformal extra symmetries can be converted into a conformal one by means of adequate field redefinitions involving the metric and the derivatives of the dilaton. Finally, by expressing the Polyakov-Liouville effective action in terms of an invariant metric, we are able to provide semiclassical models which are also invariant. This generalizes the solvable semiclassical model of Bose, Parker and Peleg (BPP) for a generic 2D dilaton gravity model.Comment: Latex, no figures. Revised version published i

Symmetries and solvable models for evaporating 2D black holes

We study the evaporation process of a 2D black hole in thermal equilibrium when the ingoing radiation is switched off suddenly. We also introduce global symmetries of generic 2D dilaton gravity models which generalize the extra symmetry of the CGHS model.Comment: 4 pages, Latex. Talk given at the Second Conference on Quantum Gravity and Constrained Dynamics. To appear in Proc. Supp. Nucl. Phys.

Heterotic strings on homogeneous spaces

We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS-NS 2-forms and gauge field fluxes. We give the general formalism and modular-invariant partition functions, then we consider some examples such as SU(2)/U(1) ~ S^2 (already described in a previous paper) and the SU(3)/U(1)^2 flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.Comment: JHEP style; 47 pages, one figur

G/G Models and W_N strings

We derive the BRST cohomology of the G/G topological model for the case of A^{(1)}_{N-1} . It is shown that at level k={p/q}-N the latter describes the (p,q) W_N minimal model coupled to $W_N$ gravity (plus some extra ``topological sectors").Comment: 17 page

DeWitt-Virasoro construction

We study a particular approach for analyzing worldsheet conformal invariance for bosonic string propagating in a curved background using hamiltonian formalism. We work in the Schrodinger picture of a single particle description of the problem where the particle moves in an infinite-dimensional space. Background independence is maintained in this approach by adopting DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum mechanics. This enables us to construct certain background independent notion of Virasoro generators, called DeWitt-Virasoro (DWV) generators, and invariant matrix elements of an arbitrary operator constructed out of them in spin-zero representation. We show that the DWV algebra is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. The actual quantum Virasoro generators should be obtained by first introducing the vacuum state and then normal ordering the DWV generators with respect to that. We demonstrate the procedure in the simple cases of flat and pp-wave backgrounds. This is a shorter version of arXiv:0912.3987 [hep-th] with many technical derivations omitted.Comment: 18 pages, shorter version of arXiv:0912.3987 [hep-th] accepted for publication in Pramana - Journal of Physic

c=1 String Theory as a Topological G/G Model

The physical states on the free field Fock space of the {SL(2,R)\over SL(2,R) model at any level are computed. Using a similarity transformation on $Q_{BRST}$, the cohomology of the latter is mapped into a direct sum of simpler cohomologies. We show a one to one correspondence between the states of the $k=-1$ model and those of the $c=1$ string model. A full equivalence between the {SL(2,R)\over SL(2,R) and {SL(2,R)\over U(1) models at the level of their Fock space cohomologies is found.Comment: 19