Gauge formulation of gravity and supergravity

[Ygor]

Hi, I have a question on the gauge formulation of gravity and supergravity.

The question that I have first concerns the gauge formulation of gravity. As I understood from various articles by Sardanashvily (see e.g. D.Ivanenko, G.Sardanashvily, The gauge treatment of gravity, Physics Reports 94 (1983) 1., or Sardanashvily, Classical gauge theory of gravity, http://arxiv.org/abs/gr-qc/0208054) gravity can be formulated as a gauge theory of the Lorentz group and the metric can then be interpreted as a goldstone field. In fact, Ivanenko & Sardanashvily point out that the gauge formulation of gravity using the Poincare group encounters a number of problems (as far as I understand it). Does anyone know the current viewpoint on the gauge formulation of gravity? Does it correspond to the formulation provided by Sardanashivly? Or are there still Poincare gauge formulations in circulation ?

Furthermore, if the claims of Sardanashvily are correct, then the supergravity theory should also be defined in terms of superbundles with the super extension of the Lorentz group, instead of the super poincare group (see www.ias.ac.in/jarch/pramana/26/00000289.pdf). Somehow, again, I have seen no mentioning of this in other literature, even though these ideas arose in the 80's. Does anyone perhaps know why? Everywhere I look, i find that one considers supergravity as a gauge theory of the superpoincare group. The question I thus have, is how is this possible in the light of the remarks that Sardanashivly makes on the gauge formulation of just gravity.

I hope anyone can shed some light on the matter.

Thanks!

Ygor

 

[AndyW]

Dear Ygor,

Thank you for your question regarding the gauge formulation of gravity and supergravity. As you have correctly noted, there are different approaches to formulating gravity as a gauge theory, with some utilizing the Poincare group and others using the Lorentz group. The current viewpoint on this issue is still a topic of debate and there are ongoing discussions in the scientific community.

Sardanashvily's work on the gauge formulation of gravity using the Lorentz group is certainly an interesting and valid approach. However, it should be noted that there are also other valid formulations using the Poincare group. In fact, many modern theories of gravity, such as general relativity and supergravity, are based on the Poincare group.

Regarding your question on the gauge formulation of supergravity, it is true that Sardanashvily proposed using the Lorentz group in the supergravity theory. However, most of the current literature on supergravity still utilizes the super Poincare group. This is because the super Poincare group has been found to be a more suitable symmetry group for supergravity, as it takes into account the additional supersymmetry and fermionic degrees of freedom.

In conclusion, while Sardanashvily's work on the gauge formulation of gravity and supergravity is certainly valuable, it is important to note that there are also other valid approaches and the scientific community is still actively exploring and debating the best formulation. I hope this helps to shed some light on the matter. Thank you for your interest in this topic.

 

[Entropia]

The gauge formulation of gravity is a mathematical framework that describes gravity as a gauge theory of the Lorentz group. This means that the gravitational force is seen as a result of the curvature of spacetime, and the metric tensor is interpreted as a goldstone field. This formulation was first proposed by D.Ivanenko and G.Sardanashvily in the 1980s and has since been studied and developed by various researchers.

One of the main advantages of this gauge formulation is that it avoids the difficulties encountered in the Poincare gauge formulation of gravity. The Poincare gauge theory, which uses the Poincare group instead of the Lorentz group, has been shown to have inconsistencies and is not as mathematically elegant as the gauge theory of the Lorentz group. As a result, the majority of research in this field has focused on the gauge formulation of gravity using the Lorentz group.

Supergravity, on the other hand, is an extension of general relativity that incorporates supersymmetry. In the gauge formulation of supergravity, the Lorentz group is extended to include supersymmetry and the theory is described in terms of superbundles. This approach was also proposed by Sardanashvily in the 1980s, but it has not gained as much attention as the superpoincare gauge formulation of supergravity.

There are a few reasons why the superpoincare gauge formulation is more commonly used. Firstly, it is more intuitive and easier to understand, as it follows the same principles as other gauge theories. Secondly, it has been shown to be a consistent and successful theory in describing gravity and supersymmetry. Finally, the superpoincare gauge formulation has been extensively studied and developed by many researchers, making it the dominant approach in the field.

In conclusion, while the gauge formulation of gravity and supergravity using the Lorentz group has been proposed and studied by Sardanashvily, the superpoincare gauge formulation remains the more widely accepted and researched approach. However, both formulations have their merits and continue to be studied and developed in order to better understand the nature of gravity and supersymmetry.