${\mathcal N}=(0,1)$ sigma model, suffers a gravitational anomaly due to the unpaired antichiral fermions. For an SCFT, the gravitational anomaly is the difference between the left- and right-moving central charges; for an SQFT, these separate central charges are not well-defined, but the total gravitational anomaly is, and is preserved under RG flow. We will normalize the gravitational anomaly so that for an SCFT with left and right moving central charges $c_L$ and $c_R$, the anomaly is $n := 2(c_R - c_L)$. The factor of $2$ is natural because then $n$ ranges over ${{\mathds}Z}$. The gravitational anomaly $n \in {{\mathds}Z}$ plays the role of homotopical degree in §\[sec.BN\], and so we will occasionally refer to it as the [*degree*]{} of the SQFT.

The gravitational anomaly manifests in various ways. First of all, it produces a nontrivial multiplier for the behaviour of the elliptic genus under the $\tau \mapsto \tau+1$, namely $Z_{RR}(\tau+1,\bar\tau+1) = e^{-2\pi i n/24} Z_{RR}(\tau,\bar\tau)$; the path integral description still guarantees that $Z_{RR}$ transforms under $\tau \mapsto -1/\tau$ with weight $(0,0)$ and some multiplier. Second, the gravitational anomaly leads to an ambiguity in the parity of “the” Ramond sector of the theory. This leads to a sign ambiguity when trying 