  We suggest the possibility that the two-dimensional SU(2)$_k$
Wess-Zumino-Witten (WZW) theory, which has global SO(4) symmetry, can be
continued to $2+\epsilon$ dimensions by enlarging the symmetry to
SO$(4+\epsilon)$. This is motivated by the three-dimensional sigma model with
SO(5) symmetry and a WZW term, which is relevant to deconfined criticality. If
such a continuation exists, the structure of the renormalization group flows at
small $\epsilon$ may be fixed by assuming analyticity in $\epsilon$. This leads
to the conjecture that the WZW fixed point annihilates with a new, unstable
fixed point at a critical dimensionality $d_c>2$. We suggest that $d_c < 3$ for
all $k$, and we compute $d_c$ in the limit of large $k$. The flows support the
conjecture that the deconfined phase transition in SU(2) magnets is a
``pseudocritical'' point with approximate SO(5), controlled by a fixed point
slightly outside the physical parameter space.
