A diff-invariant 1+1d QFT with divergent central charge?

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A discussion on the existence of a 1+1 dimensional quantum field theory (QFT) with a divergent central charge when the regularization cutoff is removed has been initiated. The conversation highlights the contribution of a free scalar field on a diff-invariant 1+1 dimensional background, specifically within the context of bosonic string theory, to the Virasoro algebra's central charge. Participants debate whether this topic is more appropriate for the Quantum Physics forum, indicating a potential overlap with quantum gravity issues.

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quelarion
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We know that a free scalar field on a diff-invariant 1+1 dimensional background (i.e. bosonic string theory on the worldsheet) contributes to the central charge of the Virasoro algebra with a constant term.

Is there any examples of a 1+1d QFT that has instead a central charge contribution that diverges when the regularization cut off is removed in the canonical quantization approach?
 
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Shoudn't this be in the Quantum Physics forum?
 
PeterDonis said:
Shoudn't this be in the Quantum Physics forum?

Well, I thought that since we are talking of a quantum gravity related problem this was the best section, but maybe you are right.
Admins, please move if you think it's better.
 

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