Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA.
Phys Rev Lett. 2013 Sep 20;111(12):121601. doi: 10.1103/PhysRevLett.111.121601. Epub 2013 Sep 17.
Large-N volume independence in circle-compactified QCD with adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories is believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the N(f) = 1 supersymmetric case. Resolution of the tension for N(f) >1 then suggests the emergence of a fermionic symmetry at large N, where there is no supersymmetry. We can escape the Coleman-Mandula theorem since the N = ∞ theory is free, with a trivial S matrix. We show an example of such a spectral degeneracy in a nonsupersymmetric toy example which has a Hagedorn spectrum.
在具有伴随 Weyl 费米子的圆紧致化 QCD 中，大 N 体积独立性意味着当半径被调谐到任意小的值时，不存在任何相变。这类理论被认为具有强子态的 Hagedorn 密度。事实证明，这些性质彼此之间明显存在紧张关系，因为状态的 Hagedorn 密度通常意味着在某个有限半径处存在相变。如果玻色子和费米子态的谱之间存在简并，就像 N(f) = 1 超对称情况下那样，这种紧张关系就会得到解决。对于 N(f) >1 的紧张关系的解决表明，在大 N 时会出现一种没有超对称性的费米子对称性。由于 N = ∞ 理论是自由的，具有平凡的 S 矩阵，因此我们可以避免 Coleman-Mandula 定理。我们在一个具有 Hagedorn 谱的非超对称玩具例子中展示了这样的谱简并的例子。
