On Theories With Light-Like Noncommutativity

TL;DR

This paper demonstrates that light-like noncommutative field theories are unitary and can be derived from string theory, exploring their properties, origins from D-branes, and their relation to known theories like SCFT and little string theories.

Contribution

It establishes the unitarity of light-like noncommutative theories and connects them to string theory limits, also analyzing their origins from D-branes and their relation to existing theories.

Findings

Light-like noncommutative theories are unitary.

Such theories can be obtained from string theory limits.

Different D-brane setups lead to distinct noncommutative theories.

Abstract

We show that field theories with light-like noncommutativity, that is with $\theta^{0i}=-\theta^{1i}$, are unitary quantum theories, and that they can be obtained as decoupled field theory limits of string theory with D-branes in a background NS-NS $B$ field. For general noncommutativity parameters, we show that noncommutative field theories which are unitary can be obtained as decoupled field theory limits of string theory, while those that are not unitary cannot be obtained from string theory because massive open strings do not decouple. We study the different theories with light-like noncommutativity which arise from Type II D-branes. The decoupling limit of the D4-brane seems to lead to a noncommutative field theory deformation of the $(2,0)$ SCFT of M5-branes, while the D5-brane case leads to a noncommutative variation of ``little string theories''. We discuss the DLCQ description of these theories.