## Séminaire de Physique Théorique

**Infinite-dimensional symmetry in non-relativistic hydrodynamics**

Ayan MUKHOPADHYAY (LPTHE)

Thursday 10 November 2011 14:00 - Tours - Salle 1180 (Bât E2)

**Résumé :**

Infinite dimensional symmetry can be realized as a symmetry of non-relativistic hydrodynamics. The symmetry is realized however, if the hydrodynamic equations are not invariant, rather if they can be made covariant under space-time transformations generated by the infinite - dimensional algebra like the Galilean Conformal Algebra (GCA). Covariance rather than invariance is necessary because most space-time transformations in the symmetry group take inertial frames to non-inertial frames. The covariant form must reduce to the standard form in a local inertial frame. We show that the Navier-Stokes equation can be covariantized if the flow is incompressible in an inertial frame. Furthermore, requiring covariance can be realized, constrains higher derivative corrections (as defined in a local inertial frame) to Navier-Stokes equation expected from a kinetic theory. We will find that covariance demands presence of a fundamental length or time scale or both. We will also give arguments via fluid/gravity correspondence that there may be gravity backgrounds which also realize such infinite-dimensional symmetry.

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