We present new rolling tachyon solutions describing the classical decay of Dbranes. Our methods are simpler than those appearing in recent works, yet our results are exact in classical string theory. The role of pressure in the decay is studied using tachyon profiles with spatial variation. In this case the final state involves an array of codimension one D-branes rather than static, pressureless tachyon matter.

We construct Euclidean 5d supersymmetric gauge theories on the five-sphere with vector and hypermultiplets. The SUSY transformation and the action are explicitly determined from the standard Noether procedure as well as from off-shell supergravity. Using localization techniques, the path-integral is shown to be restricted to the integration over a generalization of instantons on CP 2 and the Coulomb moduli.

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In this paper we give the boundary string field theory description of braneantibrane systems. From the world-sheet action of brane-antibrane systems we obtain the tachyon potential and discuss the tachyon condensation exactly. We also find the world-volume action including the gauge fields. Moreover we determine RR-couplings exactly for non-BPS branes and brane-antibranes. These couplings are written by superconnections and correspond to K 1 (M ) and K 0 (M ) for the non-BPS branes and brane-antibranes, respectively. We also show that Myers terms appear if we include the transverse scalars in the boundary sigma model action.