Old-fashioned dualities revisited

TL;DR

This paper reviews traditional dualities and extended object theories, discussing their historical context and recent applications to D-branes, phase transitions in B-F theory, and biological phenomena.

Contribution

It revisits classical dualities and explores their relevance to modern topics like D-branes and phase transitions, connecting old concepts with new developments.

Findings

Revisits 't Hooft-Mandelstam duality and its historical context.

Applies old dualities to D-branes and phase transitions in B-F theory.

Discusses novel applications to biological phenomena like microorganism swimming.

Abstract

In the lectures given at '96 Kashikojima Summer Institute, Amagi-Highland Seminars, and Yukawa Institute Workshop, the old-fashioned dualities and the theory of extended objects are reviewed, starting from 't Hooft-Mandelstam duality and following the author's old works. Application of the old-fashioned dualities to new issues are also given on the D-branes, on the phase transition of B-F theory to Einstein gravity and on the swimming of microorganisms.