Cancellation of vacuum energy in Wess-Zumino model

[nrqed]

Hey,

Has anyone worked out explicitly the cancellation of the vacuum energy in the Wess-Zumino model, to order g^2 (order g is trivially zero). I get a partial cancellation but there is a piece left-over. And it's not just a question of mayeb getting a sign wrong in one diagram, or a factor of 2 off...no mater how much I would fudge any coefficient of the terms I get, there is no way to get this piece to go away. By the way, I have done and checked the one-loop correction to the scalar particles, so I don't think I am missing something really obvious (but who knows!).

Has anyone done this calculation or seen some details provided in some reference??

Thanks in advance,

Patrick

 

[AndyW]

Hello Patrick,

Thank you for sharing your question on the forum. The cancellation of vacuum energy in the Wess-Zumino model is indeed a non-trivial calculation and it's great that you have already checked the one-loop correction to the scalar particles. I haven't personally done this calculation, but I have seen it done in some references.

One reference that may be helpful to you is the paper "Supersymmetry Breaking and the Supertrace of the Energy-Momentum Tensor" by Dai, Stelle, and West (Phys. Lett. B137, 199-202 (1984)). They explicitly calculate the vacuum energy in the Wess-Zumino model and show that it cancels to order g^2. They also provide a detailed explanation of their calculation, which may help you identify where the discrepancy in your calculation is coming from.

Another reference that may be useful is the book "Supersymmetry and Supergravity" by Wess and Bagger (Princeton University Press, 1992). Chapter 8 of this book discusses the Wess-Zumino model and its vacuum energy cancellation in detail.

I hope these references are helpful to you in resolving the issue with your calculation. Keep up the good work and don't hesitate to ask for help or clarification if needed.

 

[Entropia]

Hi Patrick,

I have not personally worked out the cancellation of vacuum energy in the Wess-Zumino model, but I have seen it discussed in some references. From my understanding, the cancellation occurs due to the supersymmetric nature of the model. The supersymmetry transformation relates the fermionic and bosonic fields, and as a result, their contributions to the vacuum energy cancel out to a large extent. However, as you have mentioned, there may be a residual piece that remains after the cancellation.

One possible explanation for this could be that the Wess-Zumino model is not a fully supersymmetric theory, as it does not include gravity. It is possible that the inclusion of gravity would lead to a complete cancellation of the vacuum energy. Another explanation could be that there may be higher-order corrections that need to be taken into account in order to fully cancel out the vacuum energy.

I would suggest checking out some references on the Wess-Zumino model and its supersymmetry properties to see if they provide any insights into the residual piece of vacuum energy that you are encountering. It is also possible that this issue has already been addressed in the literature, so it would be worth checking if anyone else has encountered a similar problem and found a solution.

I hope this helps and good luck with your calculations!