Divergent ⇒ complex amplitudes in two dimensional string theory

In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

Automated summary

Recent research has found remarkable agreement between the one instanton contribution to scattering amplitudes in two dimensional string theory and those in the matrix model. By analytically continuing external energies to imaginary values, the comparison was carried out numerically. Insights from string field theory were used to provide finite expressions for string theory amplitudes for real energies, and it was analytically shown that the imaginary parts of the string theory amplitudes reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.