Integrable supersymmetric fluid mechanics from superstrings

Bergner, Yoav; Jackiw, R.

doi:10.1016/s0375-9601(01)00305-x

Cited by 35 publications

(52 citation statements)

References 11 publications

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“…This is similar, in that respect, to the set of supersymmetric Chaplygin gas equations obtained in [17]. However, these equations are not identical to those in [17].…”

Section: Susy -B Extension Of the Polytropic Gas Dynamicssupporting

confidence: 73%

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Supersymmetric polytropic gas dynamics

Das

Popowicz

2002

Physics Letters A

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We construct the N = 1 supersymmetric extension of the polytropic gas dynamics. We give both the Lagrangian as well as the Hamiltonian description of this system. We construct the infinite set of "Eulerian" conserved charges associated with this system and show that they are in involution, thereby proving complete integrability of this system. We construct the SUSY -B extension of this system as well and comment on the similarities and differences between this system and an earlier construction of the supersymmetric Chaplygin gas. We also derive the N = 1 supersymmetric extension of the elastic medium equations, which, however, do not appear to be integrable.

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“…This is similar, in that respect, to the set of supersymmetric Chaplygin gas equations obtained in [17]. However, these equations are not identical to those in [17].…”

Section: Susy -B Extension Of the Polytropic Gas Dynamicssupporting

confidence: 73%

“…(16) and we have used the identity in Eq. (17) in the final step. This shows that the infinite set of charges are in involution thereby proving the complete integarbility of the system.…”

Section: Polytropic Gas Dynamicsmentioning

confidence: 99%

Supersymmetric polytropic gas dynamics

Das

Popowicz

2002

Physics Letters A

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“…So we begin our classification by considering the twisted one-dimensional subalgebras of g (1) ⊕ g (2) . Under the action of a oneparameter group generated by the vector field…”

Section: One-dimensional Subalgebras Of the Symmetry Superalgebras Ofmentioning

confidence: 99%

“…[1]- [4]). Recently, this method was further generalized to encompass hydrodynamic-type systems (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric versions of the equations of conformally parametrized surfaces

Bertrand¹,

Grundland²,

Hariton³

2015

J. Phys. A: Math. Theor.

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Abstract. The objective of this paper is to formulate two distinct supersymmetric (SUSY) extensions of the Gauss-Weingarten and Gauss-Codazzi (GC) equations for conformally parametrized surfaces immersed in a Grassmann superspace, one in terms of a bosonic superfield and the other in terms of a fermionic superfield. We perform this analysis using a superspace-superfield formalism together with a SUSY version of a moving frame on a surface. In constrast with the classical case, where we have three GC equations, we obtain six such equations in the bosonic SUSY case and four such equations in the fermionic SUSY case. In the fermionic case the GC equations resemble the form of the classical GC equations. We determine the Lie symmetry algebra of the classical GC equations to be infinite-dimensional and perform a subalgebra classification of the one-dimensional subalgebras of its largest finite-dimensional subalgebra. We then compute superalgebras of Lie point symmetries of the bosonic and fermionic SUSY GC equations respectively, and classify the onedimensional subalgebras of each superalgebra into conjugacy classes. We then use the symmetry reduction method to find invariants, orbits and reduced systems for two one-dimensional subalgebras for the classical case, two one-dimensional subalgebras for the bosonic SUSY case and two one-dimensional subalgebras for the fermionic SUSY case. We find explicit solutions of these reduced SUSY systems, which correspond to different surfaces immersed in a Grassmann superspace. Within this framework for the SUSY versions of the GC equations, a geometrical interpretation of the results is discussed.

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“…In the following we shall analyze the case of planar [33] and lineal [34] fluids, which devolve from the motion of membranes or strings in (3 + 1) or (2 + 1) dimensional spacetimes, respectively.…”

Section: Supersymmetric Fluid Mechanicsmentioning

confidence: 99%

Perfect fluid theory and its extensions

Jackiw¹,

Nair²,

Pi³

et al. 2004

J. Phys. A: Math. Gen.

171

255

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We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization, as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern-Simons terms (= vortex or magnetic helicity).

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Integrable supersymmetric fluid mechanics from superstrings

Cited by 35 publications

References 11 publications

Supersymmetric polytropic gas dynamics

Supersymmetric polytropic gas dynamics

Supersymmetric versions of the equations of conformally parametrized surfaces

Perfect fluid theory and its extensions

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