Symmetry reduction of 3D AdS Chern-Simons gravity on toroidal boundary yields two inequivalent 1D boundary theories: standard Schwarzian and affine-deformed Schwarzian with Kac-Moody extensions.
A Generalization of Sachdev-Ye-Kitaev
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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 $O(N_1) \times O(N_2) \times \ldots\times O(N_f)$ 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 $N$.
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UNVERDICTED 2representative citing papers
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.
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Dimensional reduction of AdS3 Chern-Simons gravity: Schwarzian and affine boundary theories
Symmetry reduction of 3D AdS Chern-Simons gravity on toroidal boundary yields two inequivalent 1D boundary theories: standard Schwarzian and affine-deformed Schwarzian with Kac-Moody extensions.
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Notes on Tensor Models and Tensor Field Theories
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.