2003/06/30 by Hitoshi Nishino, Subhash Rajpoot · 10 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Commutative property #Dimensional reduction #Dual (grammatical number) #Gauge group #Gauge theory #Integrable system #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Philosophy #Physics #Pure mathematics #Supersymmetry #Yang–Mills theory #hep-th
paper · pdf · doi:10.1016/j.physletb.2003.07.086
published in Physics Letters B 572(1-2), 91-100 (Elsevier BV) · 14 pages, no figures, minor changes with two couples of references added and deleted
arxiv created 2003/09/04 · openalex publication_date 2003/09/12 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We formulate noncommutative self-dual N=4 supersymmetric Yang–Mills theory in D=2+2 dimensions. As in the corresponding commutative case, this theory can serve as the possible master theory of all the noncommutative supersymmetric integrable models in lower dimensions. As a by-product, noncommutative self-dual N=2 supersymmetric Yang–Mills theory is obtained in D=2+2. We also perform a dimensional reduction of the N=2 theory further into N=(2,2) in D=1+1, as a basis for more general future applications. As a typical example, we show how noncommutative integrable matrix N=(1,0) supersymmetric KdV equations in D=1+1 arise from this theory, via the Yang–Mills gauge groups GL(n,R) or SL(2n,R).