nLab nearly AdS2/CFT1

Contents

Contents

Idea

The special case of AdS/CFT duality in dimensions 2/1.

References

General

General aspects of nearly AdS2-CFT1 (JT-gravity/matrix models):

SYK-model in AdS 2/CFT 1AdS_2/CFT_1

Discussion of the SYK-model as the AdS/CFT dual of JT-gravity in nearly AdS2/CFT1 and AdS-CFT in condensed matter physics:

Original articles:

Review:

Relation to black holes in terms of Majorana dimer states:

Relation to black holes in string theory and random matrix theory:

On non-perturbative effects and resurgence:

See also

Discussion of small N corrections via a lattice QFT-Ansatz on the AdS side:

  • Richard C. Brower, Cameron V. Cogburn, A. Liam Fitzpatrick, Dean Howarth, Chung-I Tan, Lattice Setup for Quantum Field Theory in AdS 2AdS_2 (arXiv:1912.07606)

See also:

  • Gregory J. Galloway, Melanie Graf, Eric Ling, A conformal infinity approach to asymptotically AdS 2×S n1AdS_2 \times S^{n-1} spacetimes (arXiv:2003.00093)

Random matrix theory in AdS 2/CFT 1AdS_2/CFT_1

On Jackiw-Teitelboim gravity dual to random matrix theory (via AdS2/CFT1 and topological recursion):

BFSS matrix model in AdS 2/CFT 1AdS_2/CFT_1

On AdS2/CFT1 with the BFSS matrix model on the CFT side and black hole-like solutions in type IIA supergravity on the AdS side:

and on its analog of holographic entanglement entropy:

See also

  • Takeshi Morita, Hiroki Yoshida, A Critical Dimension in One-dimensional Large-N Reduced Models (arXiv:2001.02109)

Flat space limit

The SYK model in flat space holography:

D1-D3 brane intersections in AdS 2/CFT 1AdS_2/CFT_1

On D1-D3 brane intersections in AdS2/CFT1:

Via T-duality from D6-D8 brane intersections:

Chord diagrams and weight systems in Physics

The following is a list of references that involve (weight systems on) chord diagrams/Jacobi diagrams in physics:

  1. In Chern-Simons theory

  2. In Dp-D(p+2) brane intersections

  3. In quantum many body models for for holographic brane/bulk correspondence:

    1. In AdS2/CFT1, JT-gravity/SYK-model

    2. As dimer/bit thread codes for holographic entanglement entropy

For a unifying perspective (via Hypothesis H) and further pointers, see:

In Chern-Simons theory

Since weight systems are the associated graded of Vassiliev invariants, and since Vassiliev invariants are knot invariants arising as certain correlators/Feynman amplitudes of Chern-Simons theory in the presence of Wilson lines, there is a close relation between weight systems and quantum Chern-Simons theory.

Historically this is the original application of chord diagrams/Jacobi diagrams and their weight systems, see also at graph complex and Kontsevich integral.

Reviewed in:

Applied to Gopakumar-Vafa duality:

  • Dave Auckly, Sergiy Koshkin, Introduction to the Gopakumar-Vafa Large NN Duality, Geom. Topol. Monogr. 8 (2006) 195-456 (arXiv:0701568)

See also

For single trace operators in AdS/CFT duality

Interpretation of Lie algebra weight systems on chord diagrams as certain single trace operators, in particular in application to black hole thermodynamics

In AdS 2/CFT 1AdS_2/CFT_1, JT-gravity/SYK-model

Discussion of (Lie algebra-)weight systems on chord diagrams as SYK model single trace operators:

  • Antonio M. García-García, Yiyang Jia, Jacobus J. M. Verbaarschot, Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N 21/N^2, JHEP 04 (2018) 146 (arXiv:1801.02696)

  • Yiyang Jia, Jacobus J. M. Verbaarschot, Section 4 of: Large NN expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs, JHEP 11 (2018) 031 (arXiv:1806.03271)

  • Micha Berkooz, Prithvi Narayan, Joan Simón, Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction, JHEP 08 (2018) 192 (arxiv:1806.04380)

following:

  • László Erdős, Dominik Schröder, Phase Transition in the Density of States of Quantum Spin Glasses, D. Math Phys Anal Geom (2014) 17: 9164 (arXiv:1407.1552)

which in turn follows

  • Philippe Flajolet, Marc Noy, Analytic Combinatorics of Chord Diagrams, pages 191–201 in Daniel Krob, Alexander A. Mikhalev,and Alexander V. Mikhalev, (eds.), Formal Power Series and Algebraic Combinatorics, Springer 2000 (doi:10.1007/978-3-662-04166-6_17)

With emphasis on the holographic content:

  • Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky, Genis Torrents, Section 5 of: Towards a full solution of the large NN double-scaled SYK model, JHEP 03 (2019) 079 (arxiv:1811.02584)

  • Vladimir Narovlansky, Slide 23 (of 28) of: Towards a Solution of Large NN Double-Scaled SYK, 2019 (pdf)

  • Micha Berkooz, Mikhail Isachenkov, Prithvi Narayan, Vladimir Narovlansky, Quantum groups, non-commutative AdS 2AdS_2, and chords in the double-scaled SYK model [arXiv:2212.13668]

and specifically in relation, under AdS2/CFT1, to Jackiw-Teitelboim gravity:

In Dpp/D(p+2)(p+2)-brane intersections

Discussion of weight systems on chord diagrams as single trace observables for the non-abelian DBI action on the fuzzy funnel/fuzzy sphere non-commutative geometry of Dp-D(p+2)-brane intersections (hence Yang-Mills monopoles):

As codes for holographic entanglement entropy

From Yan 20

Chord diagrams encoding Majorana dimer codes and other quantum error correcting codes via tensor networks exhibiting holographic entanglement entropy:

For Dyson-Schwinger equations

Discussion of round chord diagrams organizing Dyson-Schwinger equations:

  • Nicolas Marie, Karen Yeats, A chord diagram expansion coming from some Dyson-Schwinger equations, Communications in Number Theory and Physics, 7(2):251291, 2013 (arXiv:1210.5457)

  • Markus Hihn, Karen Yeats, Generalized chord diagram expansions of Dyson-Schwinger equations, Ann. Inst. Henri Poincar Comb. Phys. Interact. 6 no 4:573-605 (arXiv:1602.02550)

Review in:

  • Ali Assem Mahmoud, Section 3 of: On the Enumerative Structures in Quantum Field Theory (arXiv:2008.11661)

Last revised on January 9, 2023 at 06:18:45. See the history of this page for a list of all contributions to it.