A generalization of Sachdev-Ye-Kitaev

作者：Gross David J; Rosenhaus Vladimir

来源：The Journal of High Energy Physics, 2017, 2017(2): 093.

DOI：10.1007/JHEP02(2017)093

• 1/N Expansion
• AdS-CFT Correspondence
• Conformal Field Theory
• Matrix Models

The SYK model: fermions with a q-body, Gaussian-random, all-to-all interaction, is the first of a fascinating new class of solvable large N models. We generalize SYK to include f flavors of fermions, each occupying N-a, sites and appearing with a q(a) order in the interaction. Like SYK, this entire class of models generically has an infrared fixed point. We compute the infrared dimensions of the fermions, and the spectrum of singlet bilinear operators. We show that there is always a dimension-two operator in the spectrum, which implies that, like in SYK, there is breaking of conformal invariance and maximal chaos in the infrared four-point function of the generalized model. After a disorder average, the generalized model has a global O(N-1) x O(N-2) x ... x O(N-f) symmetry: a subgroup of the O(N) symmetry of SYK; thereby giving a richer spectrum. We also elucidate aspects of the large q limit and the OPE, and solve q = 2 SYK at finite N.

• 出版日期2017-2-17
• 单位中国科学院理论物理研究所