Symmetries and Conservation Laws of Navier—Stokes Equations

Gusyatnikova, V. N.; Yumaguzhin, V. A.

doi:10.1007/978-94-009-1948-8_3

Cited by 10 publications

(22 citation statements)

References 3 publications

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“…In fact, the algebra of invariances found there is precisely the algebra of the finite GCA (with dilatations also being an invariance when the viscous term is dropped) [8]. In fact, all the time dependent boosts are invariances of the local equations (both the Navier-Stokes and the Euler equations) [14] 2 . The Navier-Stokes equation is believed to be realized in the non-relativistic limit of the hydrodynamic regime of all quantum field theories.…”

Section: The Role Of the Gca In Physical Systemsmentioning

confidence: 98%

GCA in 2d

Bagchi

Gopakumar

Mandal

et al. 2010

J. High Energ. Phys.

179

310

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We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic conformal symmetry in 2d. Here we find quantum mechanical realisations of the (centrally extended) GCA by considering scaling limits of certain 2d CFTs. These parent CFTs are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We therefore develop, in parallel to the usual machinery for 2d CFT, many of the tools for the analysis of the quantum mechanical GCA. These include the representation theory based on GCA primaries, Ward identities for their correlation functions and a nonrelativistic Kac table. In particular, the null vectors of the GCA lead to differential equations for the four point function. The solution to these equations in the simplest case is explicitly obtained and checked to be consistent with various requirements.

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Section: The Role Of the Gca In Physical Systemsmentioning

confidence: 98%

GCA in 2d

Bagchi

Gopakumar

Mandal

et al. 2010

J. High Energ. Phys.

179

310

View full text Add to dashboard Cite

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“…It is not surprising that the choice of a temperature should break the scaling symmetry of D 7 . The interesting point is that the arbitrary accelerations M (n) i are also actually a symmetry [43] (generating what is sometimes called the Milne group [47]). Thus we have a part of the extended GCA as a symmetry of the non-relativistic Navier-stokes equation which should presumably describe the hydrodynamics in every nonrelativistic field theory.…”

Section: The Infinite Dimensional Extended Gcamentioning

confidence: 99%

Galilean conformal algebras and AdS/CFT

Bagchi

Gopakumar

2009

J. High Energy Phys.

316

481

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Non-relativistic versions of the AdS/CFT conjecture have recently been investigated in some detail. These have primarily been in the context of the Schrodinger symmetry group. Here we initiate a study based on a different nonrelativistic conformal symmetry: one obtained by a parametric contraction of the relativistic conformal group. The resulting Galilean conformal symmetry has the same number of generators as the relativistic symmetry group and thus is different from the Schrodinger group (which has fewer). One of the interesting features of the Galilean Conformal Algebra is that it admits an extension to an infinite dimensional symmetry algebra (which can potentially be dynamically realised). The latter contains a Virasoro-Kac-Moody subalgebra. We comment on realisations of this extended symmetry in a boundary field theory. We also propose a somewhat unusual geometric structure for the bulk gravity dual to any realisation of this symmetry. This involves taking a Newton-Cartan like limit of Einstein's equations in anti de Sitter space which singles out an AdS 2 comprising of the time and radial direction. The infinite dimensional Virasoro extension is identified with the asymptotic isometries of this AdS 2 .

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“…In [7], it was noted that the finite dimensional GCA is the symmetry algebra of the Euler equations. In fact, it is interesting that all the M n 's (for any n) are also symmetries of the equations [7,11]. In the introduction, we had remarked that in four dimensions, if the BMS group is not extended to include all conformal transformations, then it consists of the semi-direct product of the global conformal group in two dimensions and the supertranslations.…”

Section: The Bms 3 /Gca 2 Correspondencementioning

confidence: 99%

The BMS/GCA correspondence

Bagchi

2010

Preprint

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We find a surprising connection between asymptotically flat space-times and non-relativistic conformal systems in one lower dimension. The BMS group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is known to be infinite dimensional in three and four dimensions. We show that the BMS algebra in 3 dimensions is the same as the 2D Galilean Conformal Algebra which is of relevance to non-relativistic conformal symmetries. We further justify our proposal by looking at a Penrose limit of a radially infalling null ray inspired by nonrelativistic scaling and obtain a flat metric. The 4D BMS algebra is also discussed and found to be the same as another class of GCA, called the semi-GCA, in three dimensions. We propose a general BMS/GCA correspondence. Some consequences are discussed. Contents 1. Introduction 1 2. A quick look at the two algebras 3 2.1 The gca n algebra 3 2.2 The bms n algebra 4 3. The bms 3 /gca 2 correspondence 6 3.1 Central Charges 7 3.2 BMS from AdS: Analogies and differences 8 4. A BMN route to BMS 8 5. The bms 4 /gca s=1 3 correspondence 10 5.1 The BMS group in 4 dimensions 10 5.2 Semi-Galilean Conformal Algebras 11 6. Remarks on a general correspondence 12 7. Conclusions 13

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Symmetries and Conservation Laws of Navier—Stokes Equations

Cited by 10 publications

References 3 publications

GCA in 2d

GCA in 2d

Galilean conformal algebras and AdS/CFT

The BMS/GCA correspondence

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