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How do I reconcile the representation theoretic picture of the central charge in a CFT with the physical picture of the same?

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By a representation theoretic picture I mean viewing the central charge as something that arises as an obstruction to lifting a projective representation of the Witt algebra of the generators of conformal transformations into a linear representation, while by a physical picture I mean viewing it as something to do with the Casimir energy and the trace of the stress tensor.

asked May 27, 2014 in Theoretical Physics by Arpan Saha (50 points) [ revision history ]

One can think about more general anomalies and see the two perspectives there.  The first picture has something to do with the symmetry group (in this case the conformal group) failing to commute with certain observables (eg. the L operators). The second picture is when we compute expectation values of these operators (eg. the stress tensor) they transform under the symmetries.

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