On open superstring partition function in inhomogeneous rolling tachyon background

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.

32p, latex, v2: introduction revised to expand and correct comments on the paper by Kutasov and Niarchos, v3: corrected typos and formulas in section 4, final version to appear in JHEP

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• Note About Tachyon Kink In Nontrivial Background
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• Exact potential and scattering amplitudes from the tachyon non-linear $\beta$-function
• The Final Fate of the Rolling Tachyon
• Non-Relativistic Non-BPS Dp-brane
• Boundary String Field Theory as a Field Theory -- Mass Spectrum and Interaction
• Moduli Space of Unstable D-branes on a Circle of Critical Radius
• Applications of Thirring Model to Inhomogenous Rolling Tachyon and Dissipative Quantum Mechanics
• Tachyon Kink on non-BPS Dp-brane in the General Background
• Proposal for the Open String Tachyon Effective Action in the Linear Dilaton Background
• Note About Unstable M3-brane Action
• D-Brane Effective Actions and Particle Production near the Beginning of the Tachyon Condensation
• Rolling tachyons for separated brane-antibrane systems
• Bosonic D-brane Effective Action in Linear Dilaton Background
• Vacuum States in 2D Tachyon Effective Action