Flowing along in four dimensions
In 1988, John Cardy asked if there was a c-theorem in four dimensions. At the time, he reasonably expected his work on theories of quantum particles and fields to be professionally put to the test… But it never happened. Now – a quarter of a century later – it seems he was right.
“It is shown that, for d even, the one-point function of the trace of the stress tensor on the sphere, Sd, when suitably regularized, defines a c-function, which, at least to one loop order, is decreasing along RG trajectories and is stationary at RG fixed points, where it is proportional to the usual conformal anomaly.” said Cardy. “It is shown that the existence of such a c-function, if