nLab nearly AdS2/CFT1

Contents

Contents

Idea

The special case of AdS/CFT duality in dimensions 2/1. is called “nearly” AdS2/CFT1 because in these degenerate low dimensions the quantum field theory in duality is not quite conformal and the ambient spacetime is not quite asymptotically anti de Sitter.

References

General

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

following:

See also:

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:

Review:

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]

  • Herman Verlinde, Double-scaled SYK, Chords and de Sitter Gravity [arXiv:2402.00635]

  • Micha Berkooz, Nadav Brukner, Yiyang Jia, Ohad Mamroud, A Path Integral for Chord Diagrams and Chaotic-Integrable Transitions in Double Scaled SYK [arXiv:2403.05980]

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)

  • Paul-Hermann Balduf, Amelia Cantwell, Kurusch Ebrahimi-Fard, Lukas Nabergall, Nicholas Olson-Harris, Karen Yeats, Tubings, chord diagrams, and Dyson-Schwinger equations [arXiv:2302.02019]

Review in:

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

Other

Appearance of horizontal chord diagrams in discussion of neutrino interactions in supernovae:

  • Duff Neill, Hanqing Liu, Joshua Martin, Alessandro Roggero: Scattering Neutrinos, Spin Models, and Permutations [arXiv:2406.18677]

Last revised on July 3, 2024 at 08:31:37. See the history of this page for a list of all contributions to it.