Classical Spinning Branes in Curved Backgrounds

The dynamics of a classical branelike object in a curved background is derived from the covariant stress-energy conservation of the brane matter. The world sheet equations and boundary conditions are obtained in the pole-dipole approximation, where nontrivial brane thickness gives rise to its intrinsic angular momentum. It is shown that intrinsic angular momentum couples to both, the background curvature and the brane orbital degrees of freedom. The whole procedure is manifestly covariant with respect to spacetime diffeomorphisms and world sheet reparametrizations. In addition, two extra gauge symmetries are discovered and utilized. The examples of the point particle and the string in 4 spacetime dimensions are analyzed in more detail. A particular attention is paid to the Nambu-Goto string with massive spinning particles attached to its ends

Spinning branes in Riemann-Cartan spacetime

We use the conservation law of the stress-energy and spin tensors to study the motion of massive brane-like objects in Riemann-Cartan geometry. The world-sheet equations and boundary conditions are obtained in a manifestly covariant form. In the particle case, the resultant world-line equations turn out to exhibit a novel spin-curvature coupling. In particular, the spin of a zero-size particle does not couple to the background curvature. In the string case, the world-sheet dynamics is studied for some special choices of spin and torsion. As a result, the known coupling to the Kalb-Ramond antisymmetric external field is obtained. Geometrically, the Kalb-Ramond field has been recognized as a part of the torsion itself, rather than the torsion potential

Classical String in Curved Backgrounds

The Mathisson-Papapetrou method is originally used for derivation of the particle world line equation from the covariant conservation of its stress-energy tensor. We generalize this method to extended objects, such as a string. Without specifying the type of matter the string is made of, we obtain both the equations of motion and boundary conditions of the string. The world sheet equations turn out to be more general than the familiar minimal surface equations. In particular, they depend on the internal structure of the string. The relevant cases are classified by examining canonical forms of the effective 2-dimensional stress-energy tensor. The case of homogeneously distributed matter with the tension that equals its mass density is shown to define the familiar Nambu-Goto dynamics. The other three cases include physically relevant massive and massless strings, and unphysical tahyonic strings.Comment: 12 pages, REVTeX 4. Added a note and one referenc