Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Can somebody explain the conformal anomaly?

  1. Jul 16, 2006 #1
    String theory takes a lot of its motivation fron the conformal anomaly,
    and the way to get rid of it. Can somebody explain a non-string physicist
    what the conformal anomaly is? (Wikipedia has an article about this, but
    is has almost no content. Google search is not very helpful on the topic.)

    Since an anomaly is a quantum effect that breaks a classical symmetry, is
    there a way to make this effect tangible in the case of conformal
    symmetry?

    Is there a simple toy model, or a way to specify a simple conformal
    transformation that is broken? The conformal group is quite large after
    all; what is the simplest transformation that shows the anomaly (or do all
    of them)?

    The background of the question are a few comments from Lubos' blog, which
    are intriguing for every interested physicist. I'm just thirsty to learn
    more about the issue.

    Heinz
     
  2. jcsd
  3. Jul 18, 2006 #2
    heinrich_neumaier@yahoo.com wrote:

    > String theory takes a lot of its motivation fron the conformal anomaly,
    > and the way to get rid of it. Can somebody explain a non-string physicist
    > what the conformal anomaly is?


    I am not sring physicist but will try to explain. Situation in same sence issimilar to QED. When you
    change scale (it equivalent to comformal
    transformation) the action must be renormalized. QED - renormalizable
    theory without any additional conditions (action changes can be absorbted).
    Is the string theory we have two way: 1) critical dimention (zero conformal
    anomaly). 2) to introduce new terms in action - Liouville field.

    > Is there a simple toy model, or a way to specify a simple conformal
    > transformation that is broken? The conformal group is quite large after
    > all; what is the simplest transformation that shows the anomaly (or do all
    > of them)?


    Origing of the coformal anomaly is dependence of path integral measure
    on metric of worldsheet. We need to construct natural infinite dimentional
    form in functions space. To construct this form we can take scalar product
    defined as int u(x) v(x) sqrt(g) dx. So path integral measure naturally
    depend on metric.

    --
    --- Home Page http://ok.novgorod.net/ap ---
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Can somebody explain the conformal anomaly?
  1. Diff anomaly (Replies: 0)

Loading...