Vanishing spinor projections in supergravity

In summary, the vanishing projections obtained from the fermionic variations in the D=5 N=2 supergravity model with a time-dependent three brane have a significant physical meaning related to the preservation of supersymmetry. These projections are also connected to the symmetries of the background metric and can be interpreted as the existence of Killing spinors. Further research on supersymmetric solutions and Killing spinors is recommended for a better understanding of these implications.
  • #1
Professor_E
12
0
Hello all
I am working on a model in D=5 N=2 supergravity where the metric background is described by a time-dependent three brane, with one extra spatial dimension (a brane-world with bulk sort of set up). The vanishing of fermionic variations gives me the following weird projections:
[itex]\Gamma_t \epsilon = \Gamma_r \epsilon = \Gamma_\theta \epsilon = \Gamma_\phi \epsilon = 0[/itex]
where [itex]\Gamma[/itex] is the Dirac gamma matrix, [itex]t[/itex] is time and [itex]r,\theta,\phi[/itex] are spherical coordinates on the 3-brane. [itex]\epsilon[/itex] is the N=2 SUSY spinor.
My question is: What is the physical meaning of these vanishing projections? Any reference that addresses this and similar issues that anyone can recommend?
Thanks.
 
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  • #2


Hello, thank you for sharing your work with us. The vanishing projections you have obtained from the fermionic variations in your model have a significant physical meaning. In fact, they are related to the preservation of supersymmetry in your theory.

To understand this, let's first recall that supersymmetry is a symmetry that relates bosons and fermions, and it is crucial in many theoretical models such as supergravity. In your case, the vanishing of the fermionic variations means that the supersymmetry transformations are not changing the spinor \epsilon, i.e., they are preserving it. In other words, your model is supersymmetric.

Moreover, the specific projections you have obtained are related to the symmetries of your background metric. For example, the vanishing of \Gamma_t \epsilon indicates that the spinor \epsilon is independent of time, and similarly for the other projections. This can be interpreted as the existence of a Killing spinor, which is a special type of spinor that preserves certain symmetries of the background metric.

I would recommend looking into the literature on supersymmetric solutions in supergravity, as well as the concept of Killing spinors. This will provide you with a better understanding of the physical implications of the vanishing projections in your model. Good luck with your research!
 

1. What is the significance of vanishing spinor projections in supergravity?

Vanishing spinor projections in supergravity refer to a specific property of supergravity theories, where the supersymmetry transformations of the spinor fields vanish. This property is important because it allows for the existence of extended supersymmetry, which is necessary for the consistency of supergravity theories.

2. How are vanishing spinor projections related to supersymmetry breaking?

In supergravity theories, supersymmetry breaking occurs when the supersymmetry transformations of the spinor fields do not vanish. This is in contrast to vanishing spinor projections, where the supersymmetry transformations do vanish. Therefore, vanishing spinor projections are a necessary condition for the presence of extended supersymmetry and the absence of supersymmetry breaking.

3. Can vanishing spinor projections occur in theories without extended supersymmetry?

No, vanishing spinor projections are a consequence of extended supersymmetry. In theories without extended supersymmetry, the supersymmetry transformations of the spinor fields do not vanish, and therefore, there are no vanishing spinor projections.

4. How do vanishing spinor projections affect the behavior of supergravity theories?

Vanishing spinor projections have important implications for the structure and behavior of supergravity theories. They are related to the presence of extended supersymmetry, which affects the spectrum of particles and the interactions between them. Additionally, vanishing spinor projections play a crucial role in the formulation of supergravity theories, as they are necessary for the consistency of the theory.

5. Are there any experimental implications of vanishing spinor projections in supergravity?

Currently, there are no experimental implications of vanishing spinor projections in supergravity, as extended supersymmetry has not been observed in nature. However, vanishing spinor projections are an important aspect of theoretical models, and their study can lead to a better understanding of the structure of supergravity theories and their connections to other areas of physics, such as string theory.

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