scholarly journals A generalized Weierstrass representation of Lorentzian surfaces in ℝ2,2 and applications

2016 ◽  
Vol 13 (06) ◽  
pp. 1650074 ◽  
Author(s):  
Victor Patty
Keyword(s):  
Dimensional Space ◽  
Representation Formula ◽  
De Sitter Space ◽  
Weierstrass Representation ◽  
Spinor Representation ◽  
De Sitter ◽  
Lorentzian Surface ◽  
Lorentz Surface

We give a generalized Weierstrass formula for a Lorentz surface conformally immersed in the four-dimensional space [Formula: see text] using spinors and Lorentz numbers. We also study the immersions of a Lorentzian surface in the Anti-de Sitter space (a pseudo-sphere in [Formula: see text]): we give a new spinor representation formula and deduce the conformal description of a flat Lorentzian surface in that space.

Flat Lorentz surfaces in anti-de Sitter 3-space and Gravitational Instantons

2016 ◽  
Vol 13 (02) ◽  
pp. 1650012
Author(s):  
Jun-Ichi Inoguchi ◽  
Marianty Ionel ◽  
Sungwook Lee
Keyword(s):  
Representation Formula ◽  
Gauss Map ◽  
Conformal Structure ◽  
Weierstrass Representation ◽  
De Sitter ◽  
Gravitational Instantons ◽  
Hyperbolic Gauss Map ◽  
Monge Ampere ◽  
The Relationship ◽  
Lorentz Surface

In this paper, we study flat Lorentz surfaces in anti-de Sitter 3-space [Formula: see text] in terms of the second conformal structure. Those flat Lorentz surfaces can be represented in terms of a Lorentz holomorphic and a Lorentz anti-holomorphic data similarly to Weierstraß representation formula. An analogue of hyperbolic Gauß map is considered for timelike surfaces in [Formula: see text] and the relationship between the conformality (or the holomorphicity) of hyperbolic Gauß map and the flatness of a Lorentz surface is discussed. It is shown that flat Lorentz surfaces in [Formula: see text] are associated with a hyperbolic Monge–Ampère equation. It is also known that Monge–Ampére equation may be regarded as a 2-dimensional reduction of the Einstein’s field equation. Using this connection, we construct a class of anti-self-dual gravitational instantons from flat Lorentz surfaces in [Formula: see text].

scholarly journals A low-energy limit of Yang-Mills theory on de Sitter space

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Josh Cork ◽  
Emine Şeyma Kutluk ◽  
Olaf Lechtenfeld ◽  
Alexander D. Popov
Keyword(s):  
Dimensional Space ◽  
De Sitter Space ◽  
Low Energy ◽  
Finite Cylinder ◽  
De Sitter ◽  
Energy Limit ◽  
Compact Structure ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Infinite Dimensional

Abstract We consider Yang-Mills theory with a compact structure group G on four-dimensional de Sitter space dS4. Using conformal invariance, we transform the theory from dS4 to the finite cylinder $$ \mathcal{I} $$ I × S3, where $$ \mathcal{I} $$ I = (−π/2, π/2) and S3 is the round three-sphere. By considering only bundles P → $$ \mathcal{I} $$ I × S3 which are framed over the temporal boundary ∂$$ \mathcal{I} $$ I × S3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on ∂$$ \mathcal{I} $$ I × S3. We study the consequences of the framing on the variation of the action, and on the Yang-Mills equations. This allows for an infinite-dimensional moduli space of Yang-Mills vacua on dS4. We show that, in the low-energy limit, when momentum along $$ \mathcal{I} $$ I is much smaller than along S3, the Yang-Mills dynamics in dS4 is approximated by geodesic motion in the infinite-dimensional space $$ \mathcal{M} $$ M vac of gauge-inequivalent Yang-Mills vacua on S3. Since $$ \mathcal{M} $$ M vac ≅ C∞(S3, G)/G is a group manifold, the dynamics is expected to be integrable.

scholarly journals Gravitational turbulent instability of anti-de Sitter space

2012 ◽  
Vol 29 (19) ◽  
pp. 194002 ◽  
Author(s):  
Óscar J C Dias ◽  
Gary T Horowitz ◽  
Jorge E Santos
Keyword(s):  
De Sitter Space ◽  
De Sitter

scholarly journals Open quantum entanglement: a study of two atomic system in static patch of de Sitter space

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Samim Akhtar ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Debopam Goswami ◽  
Sudhakar Panda ◽  
...  
Keyword(s):  
Scalar Field ◽  
Density Matrix ◽  
Master Equation ◽  
Quantum Entanglement ◽  
De Sitter Space ◽  
Thermal Bath ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Open Quantum ◽  
Non Locality

Abstract In this work, our prime objective is to study non-locality and long range effect of two body correlation using quantum entanglement from various information theoretic measure in the static patch of de Sitter space using a two body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result alongwith the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely Von-Neumann entropy, R$$e'$$e′nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystem on the static patch of De-Sitter space. Finally, we have studied violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.

scholarly journals Probing Planckian physics in de Sitter space with quantum correlations

2014 ◽  
Vol 351 ◽  
pp. 872-899 ◽  
Author(s):  
Jun Feng ◽  
Yao-Zhong Zhang ◽  
Mark D. Gould ◽  
Heng Fan ◽  
Cheng-Yi Sun ◽  
...  
Keyword(s):  
De Sitter Space ◽  
Quantum Correlations ◽  
De Sitter

Static, self-dual, finite action SU(3) gauge fields in the de sitter space

1980 ◽  
Vol 96 (1-2) ◽  
pp. 105-109 ◽  
Author(s):  
A. Chakrabarti ◽  
A. Comtet ◽  
K.S. Viswanathan
Keyword(s):  
De Sitter Space ◽  
Gauge Fields ◽  
De Sitter ◽  
Finite Action
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