String Scattering from Decaying Branes

Abstract

We develop the general formalism of string scattering from decaying D-branes in bosonic string theory. In worldsheet perturbation theory, amplitudes can be written as a sum of correlators in a grand canonical ensemble of unitary random matrix models, with time setting the fugacity. An approach employed in the past for computing amplitudes in this theory involves an unjustified analytic continuation from special integer momenta. We give an alternative formulation which is well-defined for general momenta. We study the emission of closed strings from a decaying D-brane with initial conditions perturbed by the addition of an open string vertex operator. Using an integral formula due to Selberg, the relevant amplitude is expressed in closed form in terms of zeta functions. Perturbing the initial state can suppress or enhance the emission of high energy closed strings for extended branes, but enhances it for D0-branes. The closed string two point function is expressed as a sum of Toeplitz determinants of certain hypergeometric functions. A large N limit theorem due to Szego, and its extension due to Borodin and Okounkov, permits us to compute approximate results showing that previous naive analytic continuations amount to the large N approximation of the full result. We also give a free fermion formulation of scattering from decaying D-branes and describe the relation to a grand canonical ensemble for a 2d Coulomb gas.

arXiv comment36 pages, harvmac; v2: references added; v3: references added

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• Boundary States for the Rolling D-branes in NS5 Background
• Accelerating Universes and String Theory
• Non-compact String Backgrounds and Non-rational CFT
• On Superstring Disk Amplitudes in a Rolling Tachyon Background
• Supersymmetric $U(N)$ Chern-Simons-matter theory and phase transitions
• Winding effects on brane/anti-brane pairs
• A Thermodynamic Interpretation of Time for Rolling Tachyons
• The Hilbert series of U/SU SQCD and Toeplitz Determinants
• Timelike Boundary Sine-Gordon Theory and Two-Component Plasma
• The Hilbert series of N=1 SO(N_c) and Sp(N_c) SQCD, Painlevé VI and Integrable Systems
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• Remarks on the rolling tachyon BCFT
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• Brane Decay and Death of Open Strings
• New results for the SQCD Hilbert series
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• Moduli space of supersymmetric QCD in the Veneziano limit
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• Time-dependent Backgrounds in String Theory and Dualities