scholarly journals Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Alexey Milekhin
Keyword(s):  
Thermodynamic Properties ◽  
Local Operator ◽  
Residual Entropy ◽  
Point Function ◽  
Conformal Dimension ◽  
Low Energies ◽  
Non Local

Abstract We continue the investigation of coupled Sachdev-Ye-Kitaev (SYK) models without Schwarzian action dominance. Like the original SYK, at large N and low energies these models have an approximate reparametrization symmetry. However, the dominant action for reparametrizations is non-local due to the presence of irrelevant local operator with small conformal dimension. We semi-analytically study different thermodynamic properties and the 4-point function and demonstrate that they significantly differ from the Schwarzian prediction. However, the residual entropy and maximal chaos exponent are the same as in Majorana SYK. We also discuss chain models and finite N corrections.

scholarly journals Resolving modular flow: a toolkit for free fermions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Johanna Erdmenger ◽  
Pascal Fries ◽  
Ignacio A. Reyes ◽  
Christian P. Simon
Keyword(s):  
Complex Analysis ◽  
Conformal Symmetry ◽  
Standard Technique ◽  
Analytic Structure ◽  
Point Function ◽  
Free Fermions ◽  
Modular Evolution ◽  
Non Local ◽  
Kms Condition ◽  
New Formula

Abstract Modular flow is a symmetry of the algebra of observables associated to space-time regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its action beyond highly symmetric cases. The key idea of this work is to introduce a new formula for modular flows for free chiral fermions in 1 + 1 dimensions, working directly from the resolvent, a standard technique in complex analysis. We present novel results — not fixed by conformal symmetry — for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We find the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. Our ready-to-use formulae may provide new ingredients to explore the connection between spacetime and entanglement.

scholarly journals Parametrix construction for certain Lévy-type processes

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Victoria Knopova ◽  
Alexei Kulik
Keyword(s):  
Markov Process ◽  
Probability Density ◽  
Lower Bounds ◽  
Transition Probability ◽  
Local Operator ◽  
Upper And Lower Bounds ◽  
Transition Probability Density ◽  
Strong Markov Process ◽  
Non Local ◽  
Strong Markov

AbstractIn this paper, we show that a non-local operator of certain type extends to the generator of a strong Markov process, admitting the transition probability density. For this transition probability density we construct the intrinsic upper and lower bounds, and prove some smoothness properties. Some examples are provided.

scholarly journals Holographic thermal correlators revisited

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hare Krishna ◽  
D. Rodriguez-Gomez
Keyword(s):  
Black Hole ◽  
Leading Order ◽  
Point Function ◽  
Position Space ◽  
Conformal Dimension ◽  
General Contraction ◽  
Neutral Operator ◽  
Point Correlation ◽  
Leading Term ◽  
Geodesic Approximation

Abstract We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator Ok and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of TnOk (being Tn the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.

scholarly journals General Relativistic Wormhole Connections from Planck-Scales and the ER = EPR Conjecture

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 3 ◽  
Author(s):  
Fabrizio Tamburini ◽  
Ignazio Licata
Keyword(s):  
Physical Property ◽  
Space Time ◽  
The Novel ◽  
De Sitter ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Conformal Field ◽  
Low Energies ◽  
General Relativistic ◽  
Non Local

Einstein’s equations of general relativity (GR) can describe the connection between events within a given hypervolume of size L larger than the Planck length L P in terms of wormhole connections where metric fluctuations give rise to an indetermination relationship that involves the Riemann curvature tensor. At low energies (when L ≫ L P ), these connections behave like an exchange of a virtual graviton with wavelength λ G = L as if gravitation were an emergent physical property. Down to Planck scales, wormholes avoid the gravitational collapse and any superposition of events or space–times become indistinguishable. These properties of Einstein’s equations can find connections with the novel picture of quantum gravity (QG) known as the “Einstein–Rosen (ER) = Einstein–Podolski–Rosen (EPR)” (ER = EPR) conjecture proposed by Susskind and Maldacena in Anti-de-Sitter (AdS) space–times in their equivalence with conformal field theories (CFTs). In this scenario, non-traversable wormhole connections of two or more distant events in space–time through Einstein–Rosen (ER) wormholes that are solutions of the equations of GR, are supposed to be equivalent to events connected with non-local Einstein–Podolski–Rosen (EPR) entangled states that instead belong to the language of quantum mechanics. Our findings suggest that if the ER = EPR conjecture is valid, it can be extended to other different types of space–times and that gravity and space–time could be emergent physical quantities if the exchange of a virtual graviton between events can be considered connected by ER wormholes equivalent to entanglement connections.

scholarly journals N – delastic scattering at low-energies with local and non-local realistic nuclear interactions

2009 ◽  
Vol 168 ◽  
pp. 012005 ◽  
Author(s):  
L E Marcucci ◽  
L Girlanda ◽  
A Kievsky ◽  
S Rosati ◽  
M Viviani
Keyword(s):  
Nuclear Interactions ◽  
Low Energies ◽  
Non Local
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