String Organization of Field Theories: Duality and Gauge Invariance

TL;DR

This paper explores how string-like formulations of field theories can exhibit duality and gauge invariance, simplifying calculations and providing new insights into gauge theories, especially in QED.

Contribution

It demonstrates that a single string-like expression can represent the sum of many diagrams in QED, highlighting local duality and gauge invariance in field theory formulations.

Findings

Single string-like expression for QED diagrams

Simulation of duality property in string formulations

Gauge invariance preserved in dual expressions

Abstract

String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invariant while expressions for single diagrams are not.