The Hagedorn Temperature and Open QCD-String Tachyons in Pure N=1 Super Yang-Mills

TL;DR

This paper explores the relationship between Hagedorn temperature, open QCD-string tachyons, and the behavior of confining gauge theories like pure N=1 super Yang-Mills, revealing how tachyonic modes relate to the density of states.

Contribution

It introduces a novel interpretation of the divergence in potential as an open string tachyon and connects it to the Hagedorn temperature in pure N=1 super Yang-Mills theory.

Findings

Divergence in potential near critical distance r_c is linked to a tachyonic mode.

Open string tachyon presence implies exponential density of states in the UV.

Relation established between tachyon mass and Hagedorn temperature.

Abstract

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 r_c = 1/ T_H. 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 r_c 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.