  The symmetric orbifold of $\mathbb{T}^4$ was recently shown to be exactly
dual to string theory on ${\rm AdS}_3\times {\rm S}^3 \times \mathbb{T}^4$ with
minimal ($k=1$) NS-NS flux. The worldsheet theory is best formulated in terms
of the hybrid formalism of Berkovits, Vafa & Witten (BVW), in terms of which
the ${\rm AdS}_3\times {\rm S}^3$ factor is described by a
$\mathfrak{psu}(1,1|2)_k$ WZW model. At level $k=1$, $\mathfrak{psu}(1,1|2)_1$
has a free field realisation that is obtained from that of
$\mathfrak{u}(1,1|2)_1$ upon setting a $\mathfrak{u}(1)$ field, often called
$Z$, to zero. We show that the free field version of the ${\cal N}=2$
generators of BVW (whose cohomology defines the physical states) does not give
rise to an ${\cal N}=2$ algebra, but is rather contaminated by terms
proportional to the $Z$-field. We also show how to overcome this problem by
introducing additional ghost fields that implement the quotienting by $Z$.
