Rolling Tachyons and Decaying Branes

TL;DR

The paper provides exact classical rolling tachyon solutions for decaying D-branes by treating tachyon profiles as exactly marginal boundary deformations and calculating the spacetime energy-momentum tensor from disk partition functions. It shows that spatially homogeneous decays yield constant energy density with decaying pressure, i.e., pressureless tachyon matter, while spatially inhomogeneous profiles produce codimension-one D-brane arrays at a finite critical time, signaling brane formation. The authors extend these results to the superstring, where the energy density remains constant and pressure decays, and they develop a symmetry/boundary-state framework—classifying time-dependent marginal deformations and constructing boundary states at self-dual radius—to connect deformations with the resulting stress tensors. Together these results illuminate how spatial variation influences decay channels and provide a tractable, exact handle on time-dependent backgrounds in string theory via open-string disk techniques and boundary states.

Abstract

We present new rolling tachyon solutions describing the classical decay of D-branes. 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.