Kaluza-Klein Theory in Perspective

TL;DR

This paper reframes the Kaluza-Klein idea of extra spacetime dimensions from a modern, string-theoretic perspective, showing how compact internal dimensions yield four-dimensional fields and an enlarged symmetry structure. It highlights the non-abelian gauge fields arising from internal isometries and the role of dualities (T- and S-duality) in connecting KK states to broader string spectra, including extreme black holes. A central result identifies Kaluza-Klein states with extreme black holes in N=4 heterotic string theory, linking the KK spectrum to BPS bounds and duality-invariant charge lattices. Together, these insights illuminate how higher-dimensional geometry, black hole physics, and string dualities converge to constrain the spectrum and dynamics of unified theories.

Abstract

The Kaluza-Klein idea of extra spacetime dimensions continues to pervade current attempts to unify the fundamental forces, but in ways somewhat different from that originally envisaged. We present a modern perspective on the role of internal dimensions in physics, focussing in particular on superstring theory. A novel result is the interpretation of Kaluza-Klein string states as extreme black holes.(Talk delivered at the Oskar Klein Centenary Nobel Symposium, Stockholm, September 19-21, 1994.)