On k-string tensions and domain walls in N=1 gluodynamics

We discuss the k-dependence of the k-string tension σ_k in SU(N) supersymmetric gluodynamics. As is well known, at large N the k-string consists, to leading order, of k noninteracting fundamental strings, so that σ_k=kσ₁. We argue, both from field-theory and string-theory side, that subleading corrections to this formula run in powers of 1/N² rather than 1/N, thus excluding the Casimir scaling. We suggest a heuristic model allowing one to relate the k-string tension in four-dimensional gluodynamics with the tension of the BPS domain walls (k-walls). In this model the domain walls are made of a net of strings connected to each other by baryon vertices. The relation emerging in this way leads to the sine formula σ_k∼Λ²Nsinπk/N. We discuss possible corrections to the sine law, and present arguments that they are suppressed by 1/k factors. We explain why the sine law does not hold in two dimensions. Finally, we discuss the applicability of the sine formula for non-supersymmetric orientifold field theories.