On k-String Tensions and Domain Walls in N=1 Gluodynamics

Abstract

We discuss the k dependence of the k-string tension sigma_k in SU(N) supersymmetric gluodynamics. As well known, at large N the k-string consists, to leading order, of k noninteracting fundamental strings, so that sigma_k=k sigma_1. We argue, both from field-theory and string-theory side, that subleading corrections to this formula run in powers of 1/N^2 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 sigma_ k ~ Lambda^2 N sin pi k/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.

21 pages, Latex. 5 figures. v2: a factor of 2 was corrected in eq.(A.3). To appear in Nucl.Phys.B

References in corpus (4)

• Counting Domain Walls in N=1 Super Yang-Mills Theory
• String Tensions and Three Dimensional Confining Gauge Theories
• The Cosmological Constant and Domain Walls in Orientifold Field Theories and N=1 Gluodynamics
• Non-universal corrections to the tension ratios in softly broken N=2 SU(N) gauge theory

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