  The holomorphic twist provides a powerful framework to study minimally
protected sectors in supersymmetric quantum field theories. We investigate the
algebraic structure underlying the holomorphic twist of $\mathcal{N} = 1$
superconformal field theories in four dimensions. In particular, in
holomorphically twisted theories the flavour and conformal symmetry algebras
are enhanced to infinite-dimensional higher Kac Moody and higher Virasoro
symmetry algebras respectively. We explicitly compute the binary and ternary
$\lambda$-brackets and clarify their relation with the underlying
infinite-dimensional symmetry algebra. Doing so we show that the central
extensions of said symmetry algebras precisely encode the conformal anomalies
$a$ and $c$ as well as the flavour central charges of the physical
four-dimensional theory. This parallels the familiar story in two dimensions
where the conformal anomaly $c$ is encoded in the central extension of the
Virasoro algebra.
