On Conformal Theories in Four Dimensions

Abstract

Extending recent work of Kachru and Silverstein, we consider ``orbifolds'' of 4-dimensional $\mathcal{N}=4$ 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 ${\otimes }_{i}SU(N{n}_i)$ where $n_i$ 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 $\mathcal{N}=1$ and $\mathcal{N}=2$ respectively. In the $\mathcal{N}=1$ case we prove the vanishing of the beta functions to two loops.

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

References in corpus (6)

• Solutions Of Four-Dimensional Field Theories Via M Theory
• 4d Conformal Field Theories and Strings on Orbifolds
• Orbifold Resolution by D-Branes
• Fractional Branes and Wrapped Branes
• Absorption by Branes and Schwinger Terms in the World Volume Theory
• A Chiral D=4, N=1 String Vacuum with a Finite Low Energy Effective Field Theory

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