Noncommutative sine-Gordon model

✍ Scribed by O. Lechtenfeld

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 111 KB
• Volume: 53
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.200410210

✦ Synopsis

Abstract

As I briefly review, the sine‐Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self‐dual U(2) Yang‐Mills through a 2+1 dimensional integrable U(2) sigma model. I argue that the noncommutative (Moyal) deformation of this procedure should relax the algebraic reduction from U(2) → U(1) to U(2) → U(1) × U(1). The result are novel noncommutative sine‐Gordon equations for a pair of scalar fields. The dressing method is outlined for constructing its multi‐soliton solutions. Finally, I look at tree‐level amplitudes to demonstrate that this model possesses a factorizable and causal S‐matrix in spite of its time‐space noncommutativity.