Non-Abelian Moduli on Domain Walls

We study a simple model supporting domain walls which possess two orientational moduli in addition to the conventional translational modulus. This model is conceptually close to Witten's cosmic strings. We observe an $O(3)$ sigma model on the wall world volume in the low-energy limit. We solve (numerically) classical static equations of motion and find the wall profile functions and the value of the coupling of the $O(3)$ model in terms of the bulk parameters. In the second part a term describing a spin-orbit interaction in the bulk is added, which gives rise to an entanglement between rotational and translational moduli. The corresponding extra term in the low-energy Lagrangian is calculated.Comment: 11 pages, 4 figure

Infrared Renormalons in Supersymmetric Theories

I argue that in large-$N$ supersymmetric QCD infrared renormalons are absent in the conformal window, there is no need in conspiracy, and vacuum expectation values of at least some gluon operators vanish. Basing on this conclusion I conjecture that in supersymmetric gluodynamics (supersymmetric Yang-Mills theory without matter) at least the leading renormalon ambiguity disappears which would be consistent with the fact that the gluon condensate vanishes in this theory, $\langle G_{\mu\nu}^a G^{\mu\nu\,a}\rangle =0$.Comment: 16 pages, 4 figure

A note on C-Parity Conservation and the Validity of Orientifold Planar Equivalence

We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermions in vector-like - but otherwise generic - representations of the gauge group. QCD, supersymmetric Yang-Mills theory, and orientifold field theories, all belong to this class. We argue that charge conjugation is not spontaneously broken as long as Lorentz invariance is maintained. Uniqueness of the vacuum state in pure Yang-Mills theory (without fermions) and convergence of the expansion in fermion loops are key ingredients. The fact that C-invariance is conserved has an interesting application to our proof of planar equivalence between supersymmetric Yang-Mills theory and orientifold field theory on R4, since it allows the use of charge conjugation to connect the large-N limit of Wilson loops in different representations.Comment: 9 pages, LaTex. v2: minor changes, accepted to Phys.Lett.