Zero Mode Divergence Problem in String Theory

Details Zero Mode Divergence Problem in String Theory Zero Mode Divergence Problem in String Theory

1994-01-06

arxiv.org/abs/hep-th/9401013v1

Mod.Phys.Lett. A9 (1994) 2113-2122

Physics

High Energy Physics

High Energy Physics - Theory

14 pages + 2 figures (included as a uufile), LaTeX file, NSF-ITP-93-157 and UTTG-33-93

Scientific paper

For $2D$ string theory, the perturbative $S$-matrices are not well-defined due to a zero mode divergence. Although there exist formal procedures to make the integral convergent, their physical meanings are unclear. We describe a method to obtain finite $S$-matrices physically to justify the formal schemes. The scheme uses asymptotic states by wave packets which fall faster than exponentials. It is shown that the scheme gives well-defined $S$-matrices and justifies the formal shifted Virasoro-Shapiro amplitude for simple processes. The tree-level unitarity for these processes is also shown. We point out a problem in this scheme.

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