Assuming PT and Poincare invariance, a positive spectrum, and a local energy-momentum tensor, it is demonstrated that a two-dimensional QFT has a monotonically decreasing function along it's Renormalization Group flow. This is a generalization of the c theorem to theories which are not necessarily unitary.

The original c theorem is often described as `counting the degrees of freedom' as one moves along the RG flow, decreasing towards the IR as modes are integrated out. Unitary theories don't produce entropy, and so one might have imagined that RG flows are entirely reversible - but the c theorem suggests that this isn't the case. Here we see that unitarity violations (entropy generation) are also compatible with an effective c theorem, which defines a preferred direction along the RG flow.