From Super-Yang-Mills Theory to QCD: Planar Equivalence and its Implications

TL;DR

<3-5 sentence high-level summary>Planar equivalence between distinct gauge theories is developed, linking ${ m N}=1$ SYM to non-supersymmetric orientifold theories in the large-$N$ limit and enabling nonperturbative insights into QCD-like dynamics. The authors establish perturbative and nonperturbative equivalences in a common bosonic sector, map condensates across theories, and derive predictions for one-flavor QCD, the conformal window, domain walls, and chiral structures. They connect field-theory results with string theory and holographic ideas (including type-0 strings and brane constructions) to explain observed degeneracies, vanishing vacuum energy, and potential gravity duals. The work suggests a program to transfer exact SUSY results to QCD-like theories and to study lower-dimensional and multi-flavor extensions as a route toward a deeper understanding of nonperturbative gauge dynamics.

Abstract

We review and extend our recent work on the planar (large N) equivalence between gauge theories with varying degree of supersymmetry. The main emphasis is made on the planar equivalence between N=1 gluodynamics (super-Yang-Mills theory) and a non-supersymmetric "orientifold field theory." We outline an "orientifold" large N expansion, analyze its possible phenomenological consequences in one-flavor massless QCD, and make a first attempt at extending the correspondence to three massless flavors. An analytic calculation of the quark condensate in one-flavor QCD starting from the gluino condensate in N=1 gluodynamics is thoroughly discussed. We also comment on a planar equivalence involving N=2 supersymmetry, on "chiral rings" in non-supersymmetric theories, and on the origin of planar equivalence from an underlying, non-tachyonic type-0 string theory. Finally, possible further directions of investigation, such as the gauge/gravity correspondence in large-N orientifold field theory, are briefly discussed.

Figures (14)

• Figure 1: The gluino condensate $\langle \lambda\lambda\rangle$ is the order parameter labeling distinct vacua in supersymmetric gluodynamics. For the SU$(N)$ gauge group there are $N$ discrete degenerate vacua.
• Figure 2: Color decomposition of fields in the $Z_2$-orbifold daughter.
• Figure 3: Counting $N$ factors in the correlation function of the axial currents. The 't Hooft diagrams are shown in dashed lines.
• Figure 4: (a) The fermion propagator and the fermion--fermion--gluon vertex. (b) ${\cal N}=1\ $ SYM theory. (c) Orientifold daughter.
• Figure 5: (a) A typical planar contribution to the vacuum energy. (b and c) The same in the 't Hooft notation for (b) ${\cal N}=1\ $ SYM theory; (c) orientifold daughter.