Sphere Partition Functions and the Zamolodchikov Metric

Understand

We study the finite part of the sphere partition function of d-dimensional Conformal Field Theories (CFTs) as a function of exactly marginal couplings.

• In odd dimensions, this quantity is physical and independent of the exactly marginal couplings.
• In even dimensions, this object is generally regularization scheme dependent and thus unphysical.
• However, in the presence of additional symmetries, the partition function of even-dimensional CFTs can become physical.