Journal of High Energy Physics· 2017Q2
A generalization of Sachdev-Ye-Kitaev
- 318citations
- Q2SCImago
- 2017year
Short summary
Researchers generalized the Sachdev-Ye-Kitaev (SYK) model to include multiple fermion flavors (f) with varying interaction orders (q_a), revealing a universal dimension-two operator that breaks conformal invariance and implies maximal chaos.
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Key points
- The SYK model was generalized to include f flavors of fermions with varying interaction orders (q_a).
- The generalized model generically possesses an infrared fixed point.
- A dimension-two operator is always present in the spectrum, implying breaking of conformal invariance and maximal chaos.
- The generalized model exhibits a richer spectrum due to a reduced global symmetry group.
AI-generated from the title and abstract; the full text is not read.
Abstract
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) × O(N 2) × … × 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.
The authors' abstract, as published at the source. Journal of High Energy Physics, 2017 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics