Gauge invariance of complex general relativity

In this paper it is implemented how to make compatible the boundary conditions and the gauge fixing conditions for complex general relativity written in terms of Ashtekar variables using the Henneaux-Teitelboim-Vergara approach. Moreover, it is found that at first order in the gauge parameters, the Hamiltonian action is (on shell) fully gauge-invariant under the gauge symmetry generated by the first class constraints in the case when spacetime $\cal M$ has the topology ${\cal M}= R \times \Sigma$ and $\Sigma$ has no boundary. Thus, the statement that the constraints linear in the momenta do not contribute to the boundary terms is right, but only in the case when $\Sigma$ has no boundary.Comment: 9 pages, Latex file, no figures. To be published in Gen. Rel. Gra

M, Membranes, and OM

We examine the extent to which the action for the membrane of M-theory (the eleven-dimensional construct which underlies and unifies all of the known string theories) simplifies in the so-called Open Membrane (OM) limit, a limit which lies at the root of the various manifestations of noncommutativity in the string context. In order for the discussion to be relatively self-contained, we start out by reviewing why the strings of ten-dimensional string theory are in fact membranes (M2-branes) living in eleven dimensions. After that, we recall the definition of OM theory, as well as the arguments showing that it is part of a larger, eleven-dimensional structure known as Galilean or Wrapped M2-brane (WM2) theory. WM2 theory is a rich theoretical construct which is interesting for several reasons, in particular because it is essentially a toy model of M-theory. We then proceed to deduce a membrane action for OM/WM2 theory, and spell out its implications for the four different types of M2-branes one can consider in this setting. For two of these types, the action in question can be simplified by gauge-fixing to a form which implies a discrete membrane spectrum. The boundary conditions for the remaining two cases do not allow this same gauge choice, and so their dynamics remain to be unraveled.Comment: LaTeX 2e, 8 pages; aimed at phenomenologists. Invited talk given by A. Guijosa at the X Mexican School of Particles and Fields, Playa del Carmen, Mexico, November 200