String Duality--A Colloquium

TL;DR

Polchinski surveys string duality as a nonperturbative principle that equates the strongly coupled regime of one string theory with the weakly coupled regime of another, encapsulated by dual couplings $g' \sim 1/g$. The framework uncovers an eleven-dimensional limit (M-theory) in which strings and membranes unify, with D-branes and BPS states providing precise nonperturbative checks and a microscopic accounting of black hole entropy via $S_{BH} = A/(4 l_{P}^{2})$. It also suggests that gauge invariance and coupling unification can emerge from extra-dimensional dynamics, exemplified by Horava–Witten constructions that reconcile gravity with gauge forces. Overall, string duality reshapes our understanding of spacetime, quantum gravity, and unification, though fundamental questions about vacuum selection and the cosmological constant remain open and may be resolved only through a deeper nonperturbative formulation.

Abstract

The strong coupling limit of a quantum system is in general quite complicated, but in some cases a great simplification occurs: the strongly coupled limit is equivalent to the weakly coupled limit of some other system. In string theory conjectures of this type go back several years, but only in the past year and a half has it been understood to be a general principle applying to all string theories. This has improved our understanding of string dynamics, including quantum gravity, in many new and sometimes surprising ways. I describe these developments and put them in the context of the search for the unified theory of particle physics and gravity.

Figures (7)

• Figure 1: a) Leptonic weak interaction in four-fermi theory. b) The same interaction in Weinberg-Salam theory. At short distance the contact interaction is resolved into the exchange of a $W$ boson.
• Figure 2: a) Exchange of a graviton between two elementary particles. b) The same interaction in string theory. The amplitude is given by the sum over histories, over all embeddings of the string world-sheet in spacetime. The world-sheet is smooth: there is no distinguished point at which the interaction occurs (the cross section on the intermediate line is only for illustration).
• Figure 3: Space of string vacua. The cusps are limits in which a weakly coupled string description is possible (except for the M-theory limit).
• Figure 4: D-brane. Shown are two trapped strings and one not trapped.
• Figure 5: a) Long IIA string in ten dimensions. At strong coupling a perpendicular direction, which is periodic, becomes visible. b) String in eleven dimensions. c) Wrapped membrane in eleven dimensions.