Twelve-Dimensional Supersymmetric Gauge Theory as the Large N Limit

TL;DR

This paper constructs a twelve-dimensional supersymmetric gauge theory as the large N limit of ten-dimensional super Yang-Mills, revealing new dualities and a superspace formulation with extra coordinates.

Contribution

It introduces a novel twelve-dimensional supersymmetric gauge theory derived from ten-dimensional super Yang-Mills via the large N limit, with a new superspace formulation and duality insights.

Findings

Large N limit yields a 12D supersymmetric gauge theory.

Identifies extra coordinates with symplectic canonical variables.

Establishes dualities with supermembrane and superstring theories.

Abstract

Starting with the ordinary ten-dimensional supersymmetric Yang-Mills theory for the gauge group U(N), we obtain a twelve-dimensional supersymmetric gauge theory as the large N limit. The two symplectic canonical coordinates parametrizing the unitary N X N matrices for U(N) are identified with the extra coordinates in twelve dimensions in the $N\to\infty$ limit. Applying further a strong/weak duality, we get the `decompactified' twelve-dimensional theory. The resulting twelve-dimensional theory has peculiar gauge symmetry which is compatible also with supersymmetry. We also establish a corresponding new superspace formulation with the extra coordinates. By performing a dimensional reduction from twelve dimensions directly into three dimensions, we see that the Poisson bracket terms which are needed for identification with supermembrane action arises naturally. This result indicates an universal duality mechanism that the 't Hooft limit of an arbitrary supersymmetric theory promotes the original supersymmetric theory in (D-1,1) dimensions into a theory in (D,2) dimensions with an additional pair of space-time coordinates. This also indicates interesting dualities between supermembrane theory, type IIA superstring with D0-branes, and the recently-discovered twelve-dimensional supersymmetric theories.