World-Sheet Supersymmetry Without Contact Terms

TL;DR

This paper demonstrates that contact terms in fermionic string theory are not fundamental but emerge from correct treatment of superconformal geometry at puncture collisions, resolving previous inconsistencies.

Contribution

It shows that proper accounting of superconformal geometry eliminates the need for contact terms in fermionic string theory.

Findings

Contact terms are not fundamental but arise from geometric corrections.

Proper geometric treatment removes the necessity of contact interactions.

Superconformal geometry explains vertex operator collisions without contact terms.

Abstract

Green and Seiberg showed that, in simple treatments of fermionic string theory, it is necessary to introduce contact interactions when vertex operators collide. Otherwise, certain superconformal Ward identities would be violated. In this note, we show how these contact terms arise naturally when proper account is taken of the superconformal geometry involved when punctures collide. More precisely, we show that there is no contact term at all! Rather, corrections arise to the ``na\"\i ve" formula when the boundary of moduli space is described correctly.