Narrow Results

The open string ending on a flat D-brane in the pp-wave background with a constant B-field is exactly solvable but will be controlled by a more mass parameter. In this paper we mainly quantize this open string theory canonically by employing the Faddeev–Jackiw symplectic quantization procedure, and find that the phase space of the string coordinate and canonical momentum becomes fully noncummutative, consistent with the results obtained previously.

We investigate D-branes in the Nappi–Witten model. Classically symmetric D-branes are classified by the (twisted) conjugacy classes of the Nappi–Witten group, which specify the geometry of the corresponding D-branes. Quantum description of the D-branes is given by boundary states, and we need one-point functions of closed strings to construct the boundary states. We compute the one-point functions solving conformal bootstrap constraints, and check that the classical limit of the boundary states reproduces the geometry of D-branes.

Conformally recurrent pseudo-Riemannian manifolds of dimension $n\ge 5$ are investigated. The Weyl tensor is represented as a Kulkarni–Nomizu product. If the square of the Weyl tensor is non-zero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak’s theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If the square of the Weyl tensor is non-zero, the manifold is decomposable. A null recurrence vector makes the Weyl tensor of algebraic type IId or higher in the Bel–Debever–Ortaggio classification, while a time-like recurrence vector makes the Weyl tensor purely electric.

In this study, we shall try to solve the geodesic equations for some pp-wave spacetimes, which belong to a class of gravitational waves. For this purpose, the Noether symmetries of some classes of pp-waves in polar coordinates are presented. Using these symmetries, the first integrals or in other words Noether constants related to these symmetries are calculated. Finally, by means of Noether constants, the geodesic equations of the considered classes are integrated.