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Thanks.

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- Thread starter Pacopag
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Thanks.

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Hope that was of some use

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So when we say that a CFT has central charge of, say, c=2, do we really mean that the "eigenvalue" of c is 2?.

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No problem. Thanks for your help. I guess I just have to keep reading.

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Hope that was of some use

Does the notion of central charge in the context of the conformal field theory differ so radically from the notion of central charge for any other Lie algebra, like for example the Galilei or Poincare ones ? I'm just asking, because I don't see any reason, even if we complement the CFT algebra of n-dimensional space-time with SUSY generators. In other words the concept of central charge should be uniform (and essentially mathematic) for any physical Lie algebra or superalgebra.

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fzero

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Does the notion of central charge in the context of the conformal field theory differ so radically from the notion of central charge for any other Lie algebra, like for example the Galilei or Poincare ones ? I'm just asking, because I don't see any reason, even if we complement the CFT algebra of n-dimensional space-time with SUSY generators. In other words the concept of central charge should be uniform (and essentially mathematic) for any physical Lie algebra or superalgebra.

The central charge in a CFT is based on the same principle of central extension as in any other Lie algebra. The Virasoro algebra projects onto the Witt algebra when you divide by the center. Both are subalgebras of the algebra of diffeomorphisms on [tex]S^1[/tex].

There was a question about allowed values of the central charge. If we're talking about representations of the Virasoro algebra, the constraint arises from demanding that the representations be unitary (no negative norm states). All values of [tex]c\geq 1, h\geq 0[/tex] are allowed ([tex]h[/tex] is the conformal weight), while between [tex]0<c<1[/tex] there is a discrete set of points

[tex] c= 1 -\frac{6}{m(m+1)}, ~ m=3,4,\ldots .[/tex]

A blatant example of a fractional value of [tex]c[/tex] is that of a free fermion, which has [tex]c=1/2[/tex]. Ginsparg's lectures http://arxiv.org/abs/hep-th/9108028 are a great reference for many CFT topics.

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