Gauge Fields and Space-Time

TL;DR

This paper investigates a gauge/string/space-time correspondence by treating gauge-invariant words as the fundamental alphabet that maps to string vertex operators in a curved background, with the YM dynamics encoded by null states on the string worldsheet. It develops a combinatorial framework to count words, derives their on-shell constraints, and explains how higher worldsheet gauge symmetries generate relations akin to Yang-Mills equations. It then analyzes how strong coupling on the gauge side corresponds to weak curvature on the string side, proposes the existence of finite-dimension operator subsets that survive at large lambda, and discusses RR backgrounds and Thirring-like limits as routes to a controlled description. Overall, the work sketches a broad, partially concrete program toward deriving gauge dynamics and space-time structure from an underlying string-like description, including AdS/CFT-inspired geometries and matrix-model connections.

Abstract

In this article I attempt to collect some ideas,opinions and formulae which may be useful in solving the problem of gauge/ string / space-time correspondence This includes the validity of D-brane representation, counting of gauge-invariant words, relations between the null states and the Yang-Mills equations and the discussion of the strong coupling limit of the string sigma model. The article is based on the talk given at the "Odyssey 2001" conference.