Extending dualities to trialities deepens the foundations of dynamics

TL;DR

This paper proposes extending dualities to trialities to resolve conflicts with background independence, unifying fixed structures with dual variables, and illustrating this with matrix models leading to various physical theories.

Contribution

It introduces the concept of triality as an extension of duality to address background independence issues and demonstrates its application in matrix models.

Findings

Breaking triality symmetry yields different physical theories

Unification of fixed structures with dual variables

Potential explanation for dualities in quantum and string theories

Abstract

Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, and show how breaking its natural triality symmetry by imposing different compactifications yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born's duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.