Supersymmetric fluid dynamics

Abstract

Recently Navier-Stokes (NS) equations have been derived from the duality between the black branes and a conformal fluid on the boundary of AdS 5 . Nevertheless, the full correspondence has to be established between solutions of supergravity in AdS 5 and supersymmetric field theories on the boundary. That prompts the construction of NS equations for a supersymmetric fluid. In the framework of rigid susy, there are several possibilities and we propose one candidate. We deduce the equations of motion in two ways: both from the divergenless condition on the energy-momentum tensor and by a suitable parametrization of the auxiliary fields. We give the complete component expansion and a very preliminary analysis of the physics of this supersymmetric fluid.

Virtuous trees at five- and six-point levels for Yang-Mills theory and gravity

“…The tree-level BCJ representations appearing in the literature [3,4,[17][18][19][20][21][22][23][24][25][26][27][28][29] have satisfied, in addition, at most one of the two other virtues, although they may have other very favorable features such as explicit locality in external momenta, arising naturally from string-theory, compactness, or explicit forms for all multiplicity. The D-dimensional 2 tree-level representations arrived at by the Feynman rules introduced in [4] are symmetric (and local), but at the cost of fairly unwieldy expressions -embedding external-state information in polarization vectors.…”

Fermionic corrections to fluid dynamics from BTZ black hole

“…6 4 Using the forms, the gauge symmetries are obtained by shifting all fields e A → e A + ξ A , ψ → ψ + η, ω → ω AB + k AB and A → A + C and consequently the differential operator d → d + s. ξ A , η, k AB and C are the ghosts associated to diffeomorphism, supersymmetry, Lorentz symmetry and U (1) transformation, respectively and s is the BRST differential associated to those gauge symmetries. 5 We refer the reader to the vast literature on the subject for the geometry of this solution. 6 Note that the region −1 < M 0 < 0 is excluded since it corresponds to a naked singularity.…”

“…In some recent papers [4,5], we generalize that scheme to supergravity and to supersymmetric fluids on the boundary. In particular, we have to recall that AdS space is endowed with superisometries which introduce new constant parameters in the solution.…”

Plane waves in noncommutative fluids

“…The choice of the commutative fluid potentials is not unique. When it is made in terms of real functions θ(x), α(x) and β(x) it is called the Clebsch parametrization [35,36] while the fluid potentials given in terms of one real θ(x) and two complex functions z(x) andz(x), respectively, define the so called Kähler parametrization [37,38,39,40,41,42,43,44].…”