Fields in the Language of String: Divergences and Renormalization

TL;DR

This paper explores how ultraviolet divergences in quantum field theory relate to string theory, demonstrating through one-loop scalar examples that necessary counter-terms are local on the worldsheet, with implications for gauge theories.

Contribution

It introduces a string-based perspective on quantum field divergences and shows the locality of counter-terms in scalar cases, extending understanding of divergences in lightcone string formalism.

Findings

Counter-terms for scalar vertices are local on the worldsheet.

One-loop analysis confirms the translation of UV divergences to string language.

Extension to gauge fields involves additional complexities due to lightcone gauge divergences.

Abstract

This paper describes my talk given to the 27th Johns Hopkins Workshop: Symmetries and Mysteries of M Theory, G\"oteborg, Sweden, 24-26 August, 2003. After a brief introduction to the lightcone worldsheet formalism for summing the planar diagrams of field theory, I explain how the {\it uv} divergences of quantum field theory translate to the new language of string. It is shown through one loop that, at least for scalar cubic vertices, the counter-terms necessary for Poincar\'e invariance in space-time dimensions $D\leq 6$ are indeed local on the worldsheet. The extension to cover the case of gauge field vertices will be more complicated due to the extra divergences at $p^+=0$ in lightcone gauge.