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

TL;DR

This paper explores the dependence of k-string tensions in SU(N) supersymmetric gluodynamics, proposing a sine formula relation and discussing corrections, with implications for non-supersymmetric theories.

Contribution

It introduces a heuristic model linking k-string tensions to domain wall tensions, proposing the sine formula and analyzing correction suppression.

Findings

Large N limit yields noninteracting fundamental strings

Subleading corrections scale with 1/N^2, not 1/N

Sine formula for k-string tension is supported, with suppressed corrections

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.