Abstract
Supersymmetry is spontaneously broken when the field theory stress-energy tensor has a non-zero vacuum expectation value. In local supersymmetric field theories the massless gravitino and goldstino combine via the super-Higgs mechanism to a massive gravitino. We study this mechanism in four-dimensional fluids, where the vacuum expectation value of the stress-energy tensor breaks spontaneously both supersymmetry and Lorentz symmetry. We consider both constant as well as space-time dependent ideal fluids. We derive a formula for the gravitino mass in terms of the fluid velocity, energy density and pressure. We discuss some of the phenomenological implications.
Highlights
P are constant, and the fluid is in the rest frame
When the spontaneous supersymmetry breaking is due to a cosmological constant T μν = −F 2ημν, one gets from (1.1) the well known formula for the gravitino mass √ F
In this work we considered the spontaneous supersymmetry breaking triggered by the expectation value of a fluid stress-energy tensor T μν
Summary
In a global supersymmetric theory in flat space time, supersymmetry is broken spontaneously when the vacuum has non-zero energy. As a consequence of Goldstone theorem, the low energy spectrum contains a fermionic massless mode, known as the goldstino. Theories with N = 1 local supersymmetry contain a gravitino field ψμα, ψμαof spin. Parts in the decomposition of ψμα, ψμαare removed by imposing σμψμ = 0, σμψμ = 0. One can get this structure of equations and constraints from a Lagrangian. The massless gravitino Rarita-Schwinger Lagrangian is: Lψ = ǫμνρσψμσν ∂ρψσ. The field equations are ǫμνρσσν ∂ρψσ = 0, ǫμνρσσν ∂ρψσ = 0. By imposing on this equation the condition (2.3) we get σρ∂ρψσ = 0, σρ∂ρψσ = 0. It is easy to see that (2.7) and (2.3) imply (2.4)
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