Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
Confining large **N** gauge theories are believed to have a Hagedorn density of hadronic states. This results in a Hagedorn instability in the finite-temperature version of the theory, and the theory hits a deconfinement phase transition as the temperature is raised, or equivalently as the thermal circle shrinks in the Euclidean path integral formulation. However, it was recently realized that a special class of confining **4D** gauge theories, QCD with **Nf ≥ 1** adjoint massless Weyl fermions **(QCD[Adj])**, possesses large N volume independence, meaning that circle-compactified large **N QCD[Adj]** has no phase transitions as the circle size is dialed to arbitrarily small values. This property is naively in conflict with the presence of a Hagedorn density of states in these confining theories. The tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the **Nf=1** supersymmetric case. Resolution of the tension for **Nf>1** then suggests the emergence of a novel fermionic symmetry at large N, where there is no supersymmetry. Coleman-Mandula type theorems can be escaped since the **N=∞** theory is free, with a trivial S-matrix.