无序费米子、额外维和可解的杨-米尔斯理论
Disordered fermions, extra dimensions and a solvable Yang-Mills theory
摘要：
通过SU（N）矩阵推广SYK模型的无序耦合，我们建立了d+1维费米子的格点模型。费米子的积分产生了d维杨-米尔斯场的有效理论，后者在重费米子的情况下接近标准的杨-米尔斯理论，并且接近该理论的经典极限，即耦合常数为零。量子力学，该理论是解决使用大N近似的双有效理论的厄米矩阵在d维。该理论是渐近自由的，并限制了颜色。在无质量费米子的情况下，新出现的理论是渐近安全的QCD理论。我们还讨论了这个理论的SYK模型的关系。
英文摘要：
Generalizing disorder couplings of the SYK model by means of SU(N) matrices we formulate a lattice model of fermions in d+1 dimensions. Integration of fermions yields an effective theory of Yang-Mills fields in d dimensions, the latter approaching the standard Yang-Mills theory in the case of heavy fermions and the classical limit of vanishing coupling constant of the theory. Quantum mechanically, the theory is solved using large N approximation of the dual effective theory of Hermitian matrices in d dimensions. The theory is asymptotically free and confines the color. In case of massless fermions the emerging theory is an asymptotic safe QCD theory. We discuss also the relationship of this theory to the SYK model.
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