Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 306 / 2 / a

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Solution

The universal stress-tensor operator-product expansion in a two-dimensional conformal field theory is

T (z) T (w) \sim \frac{c /2}{( z - w ) ^{4}} + \frac{2 T ( w )}{( z - w ) ^{2}} + \frac{\partial T ( w )}{z - w} .

Its fourth-order coefficient defines the central charge

c

.

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