Super Yang-Mills theory in 10+2 dimensions, The 2T-physics Source for N=4 SYM and M(atrix) Theory

TL;DR

This paper constructs super Yang-Mills theory in 10+2 dimensions, revealing it as the higher-dimensional origin of lower-dimensional theories like N=4 SYM and M(atrix) theory through gauge choices and reductions.

Contribution

It introduces a 10+2 dimensional super Yang-Mills framework as the parent theory for several known lower-dimensional theories, unifying them under 2T-physics.

Findings

Establishes 10+2 super Yang-Mills as a fundamental higher-dimensional theory.

Shows how lower-dimensional theories emerge via gauge choices and reductions.

Proposes a web of connections linking 2T-physics and 1T-physics theories.

Abstract

In this paper we construct super Yang-Mills theory in 10+2 dimensions, a number of dimensions that was not reached before in a unitary supersymmetric field theory, and show that this is the 2T-physics source of some cherished lower dimensional field theories. The much studied conformally exact N=4 Super Yang-Mills field theory in 3+1 dimensions is known to be a compactified version of N=1 SYM in 9+1 dimensions, while M(atrix) theory is obtained by compactifications of the 9+1 theory to 0 dimensions (also 0+1 and others). We show that there is a deeper origin of these theories in two higher dimensions as they emerge from the new theory with two times. Pursuing various alternatives of gauge choices, solving kinematic equations and/or dimensional reductions of the 10+2 theory, we suggest a web of connections that include those mentioned above and a host of new theories that relate 2T-physics and 1T-physics field theories, all of which have the 10+2 theory as the parent. In addition to establishing the higher spacetime underpinnings of these theories, a side benefit could be that in principle our approach can be used to develop new computational techniques.