Electric-Magnetic Duality, Matrices, & Emergent Spacetime

TL;DR

This paper discusses a pre-geometric, matrix-based approach to nonperturbative String/M theory, emphasizing electric-magnetic duality and emergent spacetime geometry in the large N limit, with implications for quantum geometry and duality symmetries.

Contribution

It proposes a novel matrix Lagrangian framework that captures emergent spacetime and duality symmetries, distinguishing it from other quantum geometry proposals.

Findings

Large N limit leads to emergent spacetime geometry.

Matrix Lagrangian incorporates curved backgrounds.

O(1/N) corrections relate to string alpha' corrections.

Abstract

This is a rough transcript of talks given at the Workshop on Groups & Algebras in M Theory at Rutgers University, May 31--Jun 04, 2005. We review the basic motivation for a pre-geometric formulation of nonperturbative String/M theory, and for an underlying eleven-dimensional electric-magnetic duality, based on our current understanding of the String/M Duality Web. We explain the concept of an emerging spacetime geometry in the large N limit of a U(N) flavor matrix Lagrangian, distinguishing our proposal from generic proposals for quantum geometry, and explaining why it can incorporate curved spacetime backgrounds. We assess the significance of the extended symmetry algebra of the matrix Lagrangian, raising the question of whether our goal should be a duality covariant, or merely duality invariant, Lagrangian. We explain the conjectured isomorphism between the O(1/N) corrections in any given large N scaling limit of the matrix Lagrangian, and the corresponding alpha' corrections in a string effective Lagrangian describing some weak-coupling limit of the String/M Duality Web.