Abstract
We explore computationally tractable deformations of the SYK model. The deformed theories are described by the sum of two SYK Hamiltonians with differing numbers, q and \( \overset{\sim }{q} \), of interacting fermions. In the large N limit, employing analytic and numerical tools, we compute finite temperature correlation functions and thermodynamic quantities. We identify a novel analytically solvable model in the large q limit. We find that, under certain circumstances, the thermal RG flow in the strongly coupled infrared phase exhibits two regions of linear-in-temperature entropy, which we interpret in terms of Schwarzian actions. Using conformal perturbation theory we compute the leading relevant correction away from the intermediate near-conformal fixed point. Holographic spacetimes in two spacetime dimensions that reproduce the thermodynamics of the microphysical theory are discussed. These are flow geometries that interpolate between two Euclidean near-AdS2 spacetimes with different radii. The Schwarzian soft mode corresponding to the AdS2 region in the deep interior resides entirely within the geometric regime.
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Acknowledgments
It is a pleasure to acknowledge Alexandre Belin, Nikolay Bobev, Shira Chapman, Luca Delacretaz, Masanori Hanada, Eleanor Harris, Diego Hofman, Beatrix Mühlmann, Ben Pethybridge, Andrew Scull, and David Vegh for useful discussions. D.A. is funded by the Royal Society under the grant “The Atoms of a deSitter Universe”. The work of D.A.G. is funded by UKRI Stephen Hawking Fellowship “Quantum Emergence of an Expanding Universe”. S.U.S. is funded by the Royal Society under the grant “The Resonances of a deSitter Universe”. D.A. would like to thank the BEL center, KU Leuven and ULB for their kind hospitality during the completion of this work. D.A.G. would like to further thank the University of Amsterdam, the University of Kentucky and the Perimeter Institute for kind hospitality during the completion of this work. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. We also acknowledge the use of King’s Computational Research, Engineering and Technology Environment (CREATE) [64].
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Anninos, D., Galante, D.A. & Sheorey, S.U. Renormalisation group flows of deformed SYK models. J. High Energ. Phys. 2023, 197 (2023). https://doi.org/10.1007/JHEP11(2023)197
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DOI: https://doi.org/10.1007/JHEP11(2023)197