Holographic Complexity in dS$_{d+1}$

Jørstad, Eivind; Myers, Robert C.; Ruan, Shan-Ming

doi:10.48550/arxiv.2202.10684

Cited by 2 publications

(3 citation statements)

References 77 publications

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“…It should be pointed out that volume-complexity 1 was also introduced for some subregions in the bulk spacetime such as in a region [11,12] enclosed by a (H)RT hypersurface [13,14] or inside a Wheeler-DeWitt (WDW) patch [15]. 2 Various aspects of the CV and CA proposals have been explored extensively in the literature [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] such as: subregion complexity [50][51][52][53][55][56][57][58][59]…”

Section: Introductionmentioning

confidence: 99%

Entropy of Hawking radiation for two-sided hyperscaling violating black branes

Omidi

2022

J. High Energ. Phys.

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In this paper, we study the von Neumann entropy of Hawking radiation SR for a d + 2-dimensional Hyperscaling Violating (HV) black brane which is coupled to two Minkowski spacetimes as the thermal baths. We consider two different situations for the matter fields: first, they are described by a CFTd+2 whose central charge c is very large. Second, they are described by a d+2 dimensional HV QFT which has a holographic gravitational theory that is a HV geometry at zero temperature. For both cases, we calculate the Page curve of the Hawking radiation as well as the Page time tPage. For the first case, SR grows linearly with time before the Page time and saturates after this time. Moreover, tPage is proportional to $$ \frac{2{S}_{\mathrm{th}}}{cT} $$ 2 S th cT , where Sth and T are the thermal entropy and temperature of the black brane. For the second case, when the hyperscaling violation exponent θm of the matter fields is zero, the results are very similar to those for the first case. However, when θm ≠ 0, the entropy of Hawking radiation grows exponentially before tPage and saturates after this time. Furthermore, the Page time is proportional to log $$ \left(\frac{1}{G_{\mathrm{N},\mathrm{r}}}\right) $$ 1 G N , r , where GN,r is the renormalized Newton’s constant. It was also observed that for both cases, tPage is a decreasing and an increasing function of the dynamical exponent z and hyperscaling violation exponent θ of the black brane geometry, respectively. Moreover, for the second case, tPage is independent of zm, and for θm ≠ 0, it is a decreasing function of θm.

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Section: Introductionmentioning

confidence: 99%

Entropy of Hawking radiation for two-sided hyperscaling violating black branes

Omidi

2022

J. High Energ. Phys.

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“…Several recent studies have also explored holographic complexity and scrambling in dS space. See [67,68] for more details.…”

Section: Introductionmentioning

confidence: 99%

“…However, this depends on the "appropriate" definition of complexity. For example, the holographic complexity[68] has also shown to be divergent in specific limits.…”

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confidence: 99%

Krylov complexity in large-$q$ and double-scaled SYK model

Bhattacharjee¹,

Nandy²,

Pathak³

2022

Preprint

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Considering the large-q expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the t/q effects. The Krylov complexity naturally describes the "size" of the distribution while the higher cumulants encode richer information. We further consider the double-scaled limit of SYK q at infinite temperature, where q ∼ √ N . In such a limit, we find that the scrambling time shrinks to zero, and the Lanczos coefficients diverge. The growth of Krylov complexity appears to be "hyperfast", which is previously conjectured to be associated with scrambling in de Sitter space.

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Holographic Complexity in dS$_{d+1}$

Cited by 2 publications

References 77 publications

Entropy of Hawking radiation for two-sided hyperscaling violating black branes

Entropy of Hawking radiation for two-sided hyperscaling violating black branes

Krylov complexity in large-$q$ and double-scaled SYK model

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