On the DLCQ as a light-like limit in string theory

Details On the DLCQ as a light-like limit in string theory On the DLCQ as a light-like limit in string theory

2000-08-18

arxiv.org/abs/hep-th/0008146v2

Nucl.Phys. B591 (2000) 77-108

Physics

High Energy Physics

High Energy Physics - Theory

30 pages 13 figures eps; typos corrected. to appear in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(00)00573-3

We study the issue of defining the discrete light-cone quantization (DLCQ) in perturbative string theory as a light-like limit. While this limit is unproblematic at the classical level, it is non-trivial at the quantum level due to the divergences by the zero-mode loops. We reconsider this problem in bosonic string theory. We construct the multi-loop scattering amplitudes in both open and closed string theories by using the method of Kikkawa, Sakita and Virasoro (KSV), and then we show that these scattering amplitudes are perfectly well-defined in this limit. We also discuss the vacuum amplitudes of the string theory. They are, however, ill-defined in the light-like limit due to the zero-mode loop divergences, and hence we want supersymmetry to cure those pathological divergences even in string theory.

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