Perturbative expansion in DLCQ of field and string theories

Abstract

We explore the perturbative aspects in discrete light-cone quantization (DLCQ) of field and string theories. In field theory, we develop a systematic DLCQ perturbation and establish the Feynman rules. From the Feynman rules, we show that DLCQ S-matrix does not have a covariant continuum limit for processes with p+ = 0 exchange. Furthermore, we study the relationship between Feynman rules in (conventional) DLCQ and those in DLCQ as a light-like limit (L3) and show that the difference between DLCQ and L3 is only the existence of the divergences by the zero-mode loop diagrams in L3, which are absent in DLCQ. In string theory, we study the scattering amplitudes in L3 and discuss that at any order in perturbation, the zero-mode loop divergences are absent even in L3. This result suggests that the scattering amplitudes in L3 string theory are well-defined and coincides with those in DLCQ string theory.