Lorentz Transformation and Light-Like Noncommutative SYM

TL;DR

This paper demonstrates how Lorentz transformations can generate well-behaved light-like noncommutative super Yang-Mills theories from spatial noncommutative limits, establishing their unitarity and deriving their supergravity duals.

Contribution

It introduces a method to obtain light-like noncommutative SYM via Lorentz boosts and connects it with supergravity duals, expanding understanding of noncommutative gauge theories.

Findings

Light-like noncommutative SYM is unitary.

Supergravity duals are consistent with different noncommutative limits.

The approach unifies various noncommutative theories through Lorentz transformations.

Abstract

We show that combining the spatial noncommutative SYM limit and Lorentz transformation, one can obtain a well-behaved light-like noncommutative SYM limit. The light-like noncommutative SYM is unitary. When the boost velocity is finite, the resulting theory with space-time noncommutativity is unitary as well. The light-like noncommutative SYM limit can also be approached by combining the noncommutative open string theory limit and Lorentz transformation. Along this line, we obtain the supergravity dual for the light-like noncommutative SYM, which is the same as the one acquired using a different method. As a comparison, the supergravity duals for the ordinary SYM, spatial noncommutative SYM and the noncommutative open string theories are given as well, in an infinitely-boosted frame with finite momentum density, which are the decoupling limits of bound states (Dp, W), (D($p-2$), W, Dp), and (F1, W, Dp), respectively.