On open superstring partition function in inhomogeneous rolling tachyon background

TL;DR

This paper calculates the open superstring partition function in a time-dependent, spatially inhomogeneous tachyon background, compares it with effective actions, and examines the stress-energy tensor's conservation, shedding light on D-brane decay.

Contribution

It provides a second-order derivative computation of the partition function in an inhomogeneous tachyon background and analyzes the stress-energy tensor's conservation in this context.

Findings

Partition function computed to second order in derivatives of f.

Stress-energy tensor is conserved for linear tachyon profiles.

Insights into D-brane decay via inhomogeneous tachyon dynamics.

Abstract

We consider open superstring partition function Z on the disc in time-dependent tachyon background T= f(x_i) e^{m x_0} where the profile function f depends on spatial coordinates. We compute Z to second order in derivatives of f and compare the result with some previously suggested effective actions depending only on the first derivatives of the tachyon field. We also compute the target-space stress-energy tensor in this background and demonstrate its conservation in the ``on-shell'' case of the linear profile f= f_0 + q_i x_i corresponding to a marginal perturbation. We comment on the role of the rolling tachyon with linear spatial profile in the decay of an unstable D-brane.