1998/03/06 by A. Lawrence, Albion Lawrence, Nikita Nekrasov +3 · 9 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #Conformal field theory #Conformal map #Conformal symmetry #Conjecture #Dimension (graph theory) #Discrete group #Discrete symmetry #Field (mathematics) #Gauge group #Gauge theory #Geometry #Group (periodic table) #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quiver #hep-th
paper · pdf · doi:10.1016/s0550-3213(98)00495-7
published as Nucl.Phys. B533 (1998) 199-209 · 13 pages, uses harvmac.tex. Substantial additions made: proof of the vanishing of the 2-loop beta-functions for the N=1 models; discussion of the moduli space of couplings; discussion of S-duality for nonsupersymmetric theories; and added references
arxiv created 1998/03/06 · openalex publication_date 1998/11/01 · arxiv updated 2017/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Extending recent work of Kachru and Silverstein, we consider ``orbifolds'' of 4-dimensional N=4 SU(n) super-Yang-Mills theories with respect to discrete subgroups of the SU(4) R-symmetry which act nontrivially on the gauge group. We show that for every discrete subgroup of SU(4) there is a canonical choice of imbedding of the discrete group in the gauge group which leads to theories with a vanishing one-loop beta-function. We conjecture that these give rise to (generically non-supersymmetric) conformal theories. The gauge group is ⊗i SU(Nni) where ni denote the dimension of the irreducible representations of the corresponding discrete group; there is also bifundamental matter, dictated by associated quiver diagrams. The interactions can also be read off from the quiver diagram. For SU(3) and SU(2) subgroups this leads to superconformal theories with N=1 and N=2 respectively. In the N=1 case we prove the vanishing of the beta functions to two loops.