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IR terms from massless modes in 2D sigma model

  1. Apr 6, 2012 #1
    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,

  2. jcsd
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