Doubled Hilbert space in double-scaled SYK (2401.07403v1)
Abstract: We consider matter correlators in the double-scaled SYK (DSSYK) model. It turns out that matter correlators have a simple expression in terms of the doubled Hilbert space $\mathcal{H}\otimes\mathcal{H}$, where $\mathcal{H}$ is the Fock space of $q$-deformed oscillator (also known as the chord Hilbert space). In this formalism, we find that the operator which counts the intersection of chords should be conjugated by certain entangler'' anddisentangler''. We explicitly demonstrate this structure for the two- and four-point functions of matter operators in DSSYK.
- J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 04 (2003) 021, arXiv:hep-th/0106112.
- J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortsch. Phys. 61 (2013) 781–811, arXiv:1306.0533 [hep-th].
- M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42 (2010) 2323–2329, arXiv:1005.3035 [hep-th].
- D. K. Kolchmeyer, “von Neumann algebras in JT gravity,” JHEP 06 (2023) 067, arXiv:2303.04701 [hep-th].
- G. Penington and E. Witten, “Algebras and States in JT Gravity,” arXiv:2301.07257 [hep-th].
- M. Berkooz, N. Brukner, S. F. Ross, and M. Watanabe, “Going beyond ER=EPR in the SYK model,” JHEP 08 (2022) 051, arXiv:2202.11381 [hep-th].
- A. Goel, H. T. Lam, G. J. Turiaci, and H. Verlinde, “Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK,” JHEP 02 (2019) 156, arXiv:1807.03916 [hep-th].
- H. W. Lin and D. Stanford, “A symmetry algebra in double-scaled SYK,” SciPost Phys. 15 (2023) 234, arXiv:2307.15725 [hep-th].
- M. Berkooz, M. Isachenkov, V. Narovlansky, and G. Torrents, “Towards a full solution of the large N double-scaled SYK model,” JHEP 03 (2019) 079, arXiv:1811.02584 [hep-th].
- H. W. Lin, “The bulk Hilbert space of double scaled SYK,” JHEP 11 (2022) 060, arXiv:2208.07032 [hep-th].
- G. Vidal, “Entanglement Renormalization,” Phys. Rev. Lett. 99 no. 22, (2007) 220405, arXiv:cond-mat/0512165.
- G. Vidal, “Entanglement Renormalization: an introduction,” arXiv:0912.1651 [cond-mat.str-el].
- K. Okuyama, “Hartle-Hawking wavefunction in double scaled SYK,” JHEP 03 (2023) 152, arXiv:2212.09213 [hep-th].
- D. Stanford, “A symmetry algebra in double-scaled SYK.” Talk at It from Qubit 2023. https://pirsa.org/23080022.
- K. Okuyama, “End of the world brane in double scaled SYK,” JHEP 08 (2023) 053, arXiv:2305.12674 [hep-th].
- P. J. Szabłowski, “On the q𝑞qitalic_q-Hermite polynomials and their relationship with some other families of orthogonal polynomials,” Demonstratio Mathematica 46 (2013) 679–708.
- R. A. Askey, M. Rahman, and S. Suslov, “On a general q𝑞qitalic_q-Fourier transformation with nonsymmetric kernels,” J. Comp. Appl. Math. 68 (1996) 25–55.
- G. Gasper, “Lecture notes for an introductory minicourse on q𝑞qitalic_q-series,” arXiv:math/9509223 [math.CA].
- J. Van der Jeugt and K. Srinivasa Rao, “Invariance groups of transformations of basic hypergeometric series,” J. Math. Phys. 40 (1999) 6692–6700.
Sponsored by Paperpile, the PDF & BibTeX manager trusted by top AI labs.
Get 30 days freePaper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.