We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N = 1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N ). ⋆ Permanent address.

We study the U (N ) non-commutative Yang-Mills theory at the one-loop approximation. We check renormalizability and gauge invariance of the model and calculate the one-loop beta function. The interaction of the SU (N ) gauge bosons with the U (1) gauge boson plays an important role in the consistency check. In particular, the SU (N ) theory by itself is not consistent. We also find that the θ → 0 limit of the U (N ) theory does not converge to the ordinary SU (N ) × U (1) commutative theory, even at the planar limit. Finally, we comment on the UV/IR mixing.

We suggest a new large-N c limit for multiflavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define SUN c QCD keeping quarks in the latter. We can then define a new 1=N c expansion (at a fixed number of flavors N f ) that shares appealing properties with the topological (fixed N f =N c ) expansion while being more suitable for theoretical analysis. In particular, for N f 1, our large-N c limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to N 1 supersymmetric gluodynamics. Using known properties of the latter, we derive several qualitative and semiquantitative predictions for N f 1 massless QCD that can be easily tested in lattice simulations. Finally, we comment on possible applications for pure SU(3) Yang-Mills theory and real QCD. DOI: 10.1103/PhysRevLett.91.191601 PACS numbers: 11.15.Pg, 11.30.Pb, 12.38.Aw, 12.38.Lg Very few techniques are available for analytical studies of nonperturbative properties of nonsupersymmetric gauge theories such as QCD. Among the most promising ones, large-N expansions play a special role, in particular, because of their conjectured connection to string theories.The simplest and the oldest 1=N c expansion in QCD is that suggested by 't Hooft c . The 't Hooft expansion led to a number of notable successes in such issues as the Zweig rule, the 0 mass formula (see below), and so on. Unfortunately, nobody succeeded in fully solving QCD even to the leading order in the 't Hooft expansion.In the range of questions where the quark loops are important, a better approximation is provided by the topological expansion (TE) [2] in which N f =N c is kept fixed in the large-N c limit, rather than N f . Then, in the leading order, TE preserves all planar diagrams, including quark loops. This is easily seen by slightly modifying [2] the 't Hooft double-line notation-adding a flavor line to the single color line for quarks. In the leading (planar) diagrams the quark loops are ''empty'' inside, since gluons do not attach to the flavor line. Needless to say, obtaining analytic results in TE is even harder than in the 't Hooft case.