Interpolating between a and F


We study the dimensional continuation of the sphere free energy in conformal field theories. In continuous dimension d we define the quantity F̃ = sin(πd/2) logZ, where Z is the path integral of the Euclidean CFT on the d-dimensional round sphere. F̃ smoothly interpolates between (−1)π/2 times the a-anomaly coefficient in even d, and (−1) times the sphere… (More)