2012/10/31 by Fa-Min Chen, Yong-Shi Wu
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #BRST quantization #Black Holes and Theoretical Physics #Class (philosophy) #Gauge (firearms) #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Quiver #Simple (philosophy) #Supersymmetric gauge theory #hep-th
paper · pdf · doi:10.1007/jhep02(2013)016
published as JHEP 1302: 016, 2013 · 35 pages, minor changes, version published in JHEP
openalex publication_date 2013/02/01 · arxiv created 2013/02/10 · arxiv updated 2013/02/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we propose a special class of 3-algebras, called double-symplectic 3-algebras. We further show that a consistent contraction of the double-symplectic 3-algebra gives a new 3-algebra, called an N=4 three-algebra, which is then identified as the exact gauged three-algebra in the N=4 quiver gauge theories. A systematic construction is proposed for the 3-brackets and fundamental identities used in building up the N=4 theories, by starting with two superalgebras whose bosonic parts share at least one simple factor or U(1) factor. This leads to a systematic way of constructing D=3, N=4 quiver theories, of which several examples with new gauge groups are presented in detail. The general N=4 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be also re-derived in our new 3-algebra approach.