The bulk Hilbert space of double scaled SYK

Lin, Henry W.

doi:10.1007/jhep11(2022)060

Cited by 51 publications

(93 citation statements)

References 45 publications

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“…brane flavor sectors would lead to an interesting reconstruction theory. For a dynamical matter field which extends the pure gravity Hilbert space, avoiding ultraviolet divergences associated with matter loops on higher topologies will be crucial for defining such a theory non-perturbatively, and the results of [123,124] could be helpful in this regard.…”

Section: Jhep02(2023)195mentioning

confidence: 99%

Non-isometric quantum error correction in gravity

Kar

2023

J. High Energ. Phys.

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We construct and study an ensemble of non-isometric error correcting codes in a toy model of an evaporating black hole in two-dimensional dilaton gravity. In the preferred bases of Euclidean path integral states in the bulk and Hamiltonian eigenstates in the boundary, the encoding map is proportional to a linear transformation with independent complex Gaussian random entries of zero mean and unit variance. Using measure concentration, we show that the typical such code is very likely to preserve pairwise inner products in a set S of states that can be subexponentially large in the microcanonical Hilbert space dimension of the black hole. The size of this set also serves as an upper limit on the bulk effective field theory Hilbert space dimension. Similar techniques are used to demonstrate the existence of state-specific reconstructions of S-preserving code space unitary operators. State-specific reconstructions on subspaces exist when they are expected to by entanglement wedge reconstruction. We comment on relations to complexity theory and the breakdown of bulk effective field theory.

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Section: Jhep02(2023)195mentioning

confidence: 99%

Non-isometric quantum error correction in gravity

Kar

2023

J. High Energ. Phys.

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“…Note that the Liouville action had a larger diff(S 1 ) × diff(S 1 ) symmetry, of which only SL(2, R) diag is preserved by the solution. We give some more details about this symmetry in appendix A (see also [29]). The remaining task is to find (F IJ , G IJ ) such that the solution respects the symmetry and the boundary condition of g IJ .…”

Section: Thermal Solutionmentioning

confidence: 99%

Effective description of sub-maximal chaos: stringy effects for SYK scrambling

Choi¹,

Haehl²,

Sárosi³

2023

Preprint

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It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective 'scramblon' modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with submaximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.

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“…DS-SYK has recently been conjectured to be dual to gravity on de-sitter spacesee [35][36][37][38][39]. For other works on DS-SYK see [40][41][42][43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

“…The reason it is useful to do this is because while initially the chord diagrams looked like a convenient combinatorial tool to solve the SYK model in the double scaling limit, recent works indicate that the chord diagrams could be more directly related to the bulk gravitational theory. In particular, [48] showed that the Hilbert space of (sliced open) chord diagram is the same as two sided wormhole Hilbert space and also [34] showed that the chord diagrams can be related to the boundary particle moving in the dual AdS 2 . Given such interpretations, it might be worthwhile to explore the structure of chord diagrams in various individual models so that the connections to the dual gravitational picture might be better explored.…”

Section: Introductionmentioning

confidence: 99%

SYK Model with global symmetries in the double scaling limit

Narayan¹,

Swathi²

2023

Preprint

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We discuss the double scaling limit of the SYK model with global symmetries. We develop the chord diagram techniques to compute the moments of the Hamiltonian and the two point function in the presence of arbitrary chemical potential. We also derive a transfer matrix acting on an auxilliary hilbert space which can capture the chord diagram contributions. We present explicit results for the case of classical group symmetries namely orthogonal, unitary and symplectic groups. We also find the partition functions at fixed charges.

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The bulk Hilbert space of double scaled SYK

Cited by 51 publications

References 45 publications

Non-isometric quantum error correction in gravity

Non-isometric quantum error correction in gravity

Effective description of sub-maximal chaos: stringy effects for SYK scrambling

SYK Model with global symmetries in the double scaling limit

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