D1-brane with overcritical electric field in AdS₃and S-brane

Abstract

We study aspects of Dirichlet S-branes, which are defined as Dirichlet boundary condition on a time like embedding of open strings, in general backgrounds. By applying T -duality along an isometry of the unphysical dS 2 -branes in NS-NS supported AdS 3 -background, we find S0-brane. We also study the time dependent tachyon condensation on the unstable Dp-brane and interpret the singular solutions as lower dimensional S(p-1)-brane that couples to real Ramond-Ramond fields while to imaginary NS-NS modes.

Geometrical dynamics of Born–Infeld objects

“…Equation ( 76) is in agreement with the energy computed in [19], and is equivalent to the energy density ε 1 obtained above (see (19)). It is important to mention that this energy can also be obtained directly (up to a constant term) by taking the zero-th component of the momentum P µ obtained in the ADM decomposition (equation ( 36)).…”

“…Further, we will assume that on the worldsheet lives the U(1) gauge field A a = (A 0 , A 1 ) = (0, A θ 1 ) with a, b = t, θ 1 . Physically, this is a D1-brane with overcritical electric fields that wraps in θ 1 direction, as discussed in [18,19]. The components of the induced metric are given by…”

“…Under an infinitesimal deformation of the embedding functions X → X + δX as well as A → A + δA, the first variation of the action (1) casts out the equations of motion associated with the configuration space C [19,22],…”

“…In section 5 we write Hamilton's equations of motion in terms of the geometrical quantities described previously. We put our machinery at work by considering an unambiguous example in section 6 in an anti-de Sitter background previously analysed using a different approach in [18,19]. Section 7 presents some concluding remarks and some perspectives on the quantum approach.…”