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- W4313305515 abstract "We study the double-scaling limit of SYK (DS-SYK) model and elucidate the underlying quantum group symmetry. The DS-SYK model is characterized by a parameter $q$, and in the $qrightarrow 1$ and low-energy limit it goes over to the familiar Schwarzian theory. We relate the chord and transfer-matrix picture to the motion of a ``boundary particle on the Euclidean Poincar{'e} disk, which underlies the single-sided Schwarzian model. $AdS_2$ carries an action of $mathfrak{s}mathfrak{l}(2,{mathbb R}) simeq mathfrak{s}mathfrak{u}(1,1)$, and we argue that the symmetry of the full DS-SYK model is a certain $q$-deformation of the latter, namely $mathcal{U}_{sqrt q}(mathfrak{s}mathfrak{u}(1,1))$. We do this by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a lattice deformation of $AdS_2$, which has this $mathcal{U}_{sqrt q}(mathfrak{s}mathfrak{u}(1,1))$ algebra as its symmetry. We also exhibit the connection to non-commutative geometry of $q$-homogeneous spaces, by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a non-commutative deformation of $AdS_3$. There are families of possibly distinct $q$-deformed $AdS_2$ spaces, and we point out which are relevant for the DS-SYK model." @default.
- W4313305515 created "2023-01-06" @default.
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- W4313305515 date "2022-12-27" @default.
- W4313305515 modified "2023-09-27" @default.
- W4313305515 title "Quantum groups, non-commutative $AdS_2$, and chords in the double-scaled SYK model" @default.
- W4313305515 doi "https://doi.org/10.48550/arxiv.2212.13668" @default.
- W4313305515 hasPublicationYear "2022" @default.
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