IR terms from massless modes in 2D sigma model

[nidnus]

Hi All,

My first post here.

As far as I've understood there are problems with massless states in two dimensions.

In the problem I am working on I have a 2D (non linear) sigma model with a lot of symmetries. The worldsheet fields come as heavy and massless. My main interest is to compute one (and perhaps higher) loop corrections to the bare masses. However, for loops where a massless and a massive field propagates I find that there are IR divergent term that don't cancel (these originate from 3 vertex bubble diagrams). While the symmetries are enough to make all UV terms cancel, this seem not to be the case for the IR terms. My question is, what is the meaning of this? How should I interpret this result? Oddly this loop correction is for a massive state. The loop correction to the massless modes do not suffer from these IR terms (but then, I don't have any massless fields running in bubble diagrams). Is this a sign that my sigma model is inconsistent or is something that should be expected (and more importantly, can be ignored). If yes, then what is the argument for that?

Thanks a lot,

Nid.

 

[AndyW]

Dear Nid,

Thank you for posting your question. The issue you are facing with IR divergent terms in your 2D sigma model is a common problem in theoretical physics, and it is important to address it in order to understand the validity of your results.

In general, IR (infrared) divergences arise when the energy or momentum of a particle becomes very small or zero. In your case, it seems that these IR divergences are arising due to the presence of both massive and massless fields in your loop diagrams. This can happen when the massless field has a small or zero momentum, leading to a divergence in the loop integral.

One way to interpret this result is that the symmetries of your theory are not enough to fully cancel out these IR divergences. This could indicate that your sigma model is not consistent, or that there may be some missing ingredients in your calculations.

In order to determine the validity of your results, it is important to carefully examine the symmetries of your theory and the calculations you are doing. It may also be helpful to compare your results with other similar models or to consult with other experts in the field.

In some cases, IR divergences can be ignored if they can be shown to cancel out in the final physical result. However, this must be carefully justified and cannot be assumed without proper analysis.

I hope this helps to answer your question. Good luck with your research and feel free to post any further questions or updates on your progress.