Gravity dual of the Ising model

Castro, Alejandra; Gaberdiel, Matthias R.; Hartman, Thomas; Maloney, Alexander; Volpato, Roberto

doi:10.1103/physrevd.85.024032

Cited by 80 publications

(186 citation statements)

References 75 publications

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“…11) compared to the simulation without obliquity dependency, and, hence, to an effective acceleration parameter of η e 0.15. Therefore, there is a lower amount of CRs produced in the shock, and as expected from Chevalier (1983) (see also Castro et al 2011;Bell 2015), the exact solution is now better reproduced for a lower effective adiabatic index of γ e = 1.55 (see Fig. 12) and leads to a shock front in advance compared to the obliquity-independent simulation.…”

Section: The 3d Sedov Explosionmentioning

confidence: 66%

“…There is a large body of evidence for CRs accelerated in the shocked-shell material of supernova (SN) explosions (e.g. Koyama et al 1995;Decourchelle et al 2000;Aharonian et al 2004;Warren et al 2005;Helder et al 2009;Ackermann et al 2013) and it is shown that they have a significant impact on the shell structure and dynamics (Chevalier 1983;Dorfi 1990;Zank et al 1993;Wagner et al 2009;Ferrand et al 2010;Castro et al 2011;Pfrommer et al 2017;Pais et al 2018;Diesing & Caprioli 2018). SN remnants (SNR) are expected to be the main source of CRs permeating the entire interstellar medium (ISM) of galaxies (Aguilar et al 2015), though the consistency of the accelerated CR spectrum in SNR with that of entire galaxies is still intensely debated (see Blasi 2013 for a review).…”

Section: Introductionmentioning

confidence: 99%

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Shock-accelerated cosmic rays and streaming instability in the adaptive mesh refinement code Ramses

Dubois

Commerçon

Marcowith

et al. 2019

A&A

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Cosmic rays (CRs) are supposed to play a dynamical important role on several key aspects of galaxy evolution, including the structure of the interstellar medium, the formation of galactic winds, and the non-thermal pressure support of halos. We introduce a numerical model solving for the CR streaming instability and acceleration of CRs at shocks with a fluid approach in the adaptive mesh refinement code ramses. CR streaming is solved with a diffusion-like approach and its anisotropic nature is naturally captured. We introduce a shock finder for the ramses code that automatically detects shock discontinuities in the flow. Shocks are the loci for CR injection, and their efficiency of CR acceleration is made dependent of the upstream magnetic obliquity according to the diffuse shock acceleration mechanism. We show that the shock finder accurately captures shock locations and estimates the shock Mach number for several problems. The obliquity-dependent injection of CRs in the Sedov solution leads to situations where the supernova bubble exhibits large polar caps (homogeneous background magnetic field), or a patchy structure of the CR distribution (inhomogeneous background magnetic field). Finally, we combine both accelerated CRs with streaming in a simple turbulent interstellar medium box, and show that the presence of CRs significantly modify the structure of the gas.

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Section: The 3d Sedov Explosionmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Shock-accelerated cosmic rays and streaming instability in the adaptive mesh refinement code Ramses

Dubois

Commerçon

Marcowith

et al. 2019

A&A

View full text Add to dashboard Cite

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“…The equations of motion (4.1) are then recognized as the Lax equations 20) where the subindex + indicates the truncation to non-negative powers of ∂ + only. The factor of µ can be absorbed into a redefinition of x − .…”

Section: Commuting Charges From the Kdv Hierarchymentioning

confidence: 99%

“…Partition functions have been computed in [15,16], and three point functions have been checked in [7,[17][18][19]. Other aspects of the duality have been investigated extensively [20][21][22][23][24][25], see [26] for a review.…”

Section: Introductionmentioning

confidence: 99%

$ \mathcal{W} $ symmetry and integrability of higher spin black holes

Compère

Song²

2013

J. High Energ. Phys.

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We obtain the asymptotic symmetry algebra of sl(3, R) × sl(3, R) Chern-Simons theory with Dirichlet boundary conditions for fixed chemical potential. These boundary conditions are obeyed by higher spin black holes. For each embedding of sl(2, R) into sl(3, R), we show that the asymptotic symmetry group is independent of the chemical potential. On the one hand, starting from AdS 3 in the principal embedding, we show that the W 3 × W 3 symmetry is preserved upon turning on perturbatively spin 3 chemical potentials. On the other hand, starting from AdS 3 in the diagonal embedding, we show that the W (2) 3 ×W (2) 3 symmetry is preserved upon turning on finite spin 3/2 chemical potentials. We also make connections between the canonical Lagrangian formalism and integrability methods based on the n = 3 KdV (Boussinesq) hierarchy.

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“…This is very similar in spirit to the proposal of[10] to compute partition functions from vacuum characters.…”

mentioning

confidence: 55%

Crossing, modular averages and N ↔ k in WZW models

Mahanta

Maharana

2019

J. High Energ. Phys.

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We consider the construction of genus zero correlators of SU (N ) k WZW models involving two Kac Moody primaries in the fundamental and two in the anti-fundamental representation from modular averaging of the contribution of the vacuum conformal block. In cases where we find the orbit of the vacuum conformal block to be finite, modular averaging reproduces the exact result for the correlators. In other cases, we perform the modular averaging numerically, the results are in agreement with the exact answers. We find a close relationship between the modular averaging sums of the theories related by level rank duality. We establish a one to one correspondence between elements of the orbits of the vacuum conformal blocks of dual theories. The contributions of paired terms to their respective correlators are simply related. One consequence of this is that the ratio between the OPE coefficients associated with dual correlators can be obtained analytically without performing the sums involved in the modular averagings. The pairing of terms in the modular averaging sums for dual theories suggests an interesting connection between level rank duality and semi-classical holographic computations of the correlators in the theories.

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Gravity dual of the Ising model

Cited by 80 publications

References 75 publications

Shock-accelerated cosmic rays and streaming instability in the adaptive mesh refinement code Ramses

Shock-accelerated cosmic rays and streaming instability in the adaptive mesh refinement code Ramses

$ \mathcal{W} $ symmetry and integrability of higher spin black holes

Crossing, modular averages and N ↔ k in WZW models

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