The Hagedorn temperature and open QCD-string tachyons in pure N=1 super-Yang-Mills

We consider large-N confining gauge theories with a Hagedorn density of states. In such theories the potential between a pair of colour-singlet sources may diverge at a critical distance rc=1/TH. We consider, in particular, pure N=1 super-Yang-Mills theory and argue that when a domain wall and an anti-domain wall are brought to a distance near rc the interaction potential is better described by an “open QCD-string channel”. We interpret the divergence of the potential in terms of a tachyonic mode and relate its mass to the Hagedorn temperature. Finally we relate our result to a theorem of Kutasov and Seiberg and argue that the presence of an open string tachyonic mode in the annulus amplitude implies an exponential density of states in the UV of the closed string channel.