Gauging the complex SYK model

Abstract

Motivated by SYK-like models describing near-BPS black holes in string/M-theory, we consider gauging the U$(1)$ symmetry of the complex SYK model in the presence of a Wilson line with charge $k$. At a fixed background gauge field, solutions to the Schwinger-Dyson equations display vastly different properties from those at a fixed real chemical potential. In the partition function and the two-point function, the integral over the gauge field is performed either directly or via a large $N$ saddle point approximation, and both results are consistent with exact diagonalization data. From the behaviour of the two-point function at large $N$, we deduce that the conformal symmetry at low energies is preserved at fixed $\kappa =k/N=0$, but broken at $\kappa \ne 0$. In addition, we find that there is maximal chaos for all $k$.

clarifications added, typos corrected

References in corpus (33)

• A bound on chaos
• Comments on the Sachdev-Ye-Kitaev model
• On the Geometry of the String Landscape and the Swampland
• An Investigation of AdS${}_2$ Backreaction and Holography
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• Non-Fermi liquid regime of a doped Mott insulator
• Supersymmetric AdS_4 black holes and attractors
• Bi-Local Holography in the SYK Model
• More on Supersymmetric and 2d Analogs of the SYK Model
• Notes on the complex Sachdev-Ye-Kitaev model
• Witten Index and Wall Crossing
• The string origin of dyonic $\mathcal{N}=8$ supergravity and its simple Chern-Simons duals
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• Euclidean Black Saddles and AdS${}_4$ Black Holes
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Looking at supersymmetric black holes for a very long time
• Vector models and generalized SYK models
• Phases Of Melonic Quantum Mechanics
• BPS black hole horizons from massive IIA
• BPS black holes from massive IIA on S${}^6$
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• Disordered vector models: from higher spins to incipient strings
• The shared universality of charged black holes and the many many-body SYK model
• A quantum mechanics for magnetic horizons
• Chiral Algebras of Two-Dimensional SYK Models
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Soft modes in $\mathcal{N}=2$ SYK model