Space-filling branes of gravitational ancestry

Abstract

We introduce a new kind of space-filling brane, which we term "G-brane" because its action is a descendant of the gravitational action. The G-brane may be thought of as the remanent of the gravitational field when the propagating gravitons are removed. The G-brane is different from the Dirac or Nambu space-filling branes. Its properties in any spacetime dimension D are exhibited. When the spacetime dimension D is greater than or equal to three, the G-brane does not possess propagating degrees of freedom, just as the Dirac or Nambu branes. For D=3 the G-brane yields a reformulation of gravitation theory in which the Hamiltonian constraints can be solved explicitly, while keeping the spacetime structure manifest. For D=2 the G-brane provides a realization of the conformal algebra, i.e. a conformal field theory, in terms of two scalar fields and their conjugates, which possesses a classical central charge. In the G-brane reformulation of (2+1) gravity, the boundary degrees of freedom of the gravitational field in asymptotically anti-de Sitter space appear as "matter" coupled to the (1+1) G-brane on the boundary.