  We prove that the dynamical sine-Gordon equation on the two dimensional torus
introduced in [HS16] is locally well-posed for the entire subcritical regime.
At first glance this equation is far out of the scope of the local existence
theory available in the framework of regularity structures [Hai14, BHZ16, CH16,
BCCH17] since it involves a non-polynomial nonlinearity and the solution is
expected to be a distribution (without any additional small parameter as in
[FG17, HX18]). In [HS16] this was overcome by a change of variable, but the new
equation that arises has a multiplicative dependence on highly non-Gaussian
noises which makes stochastic estimates highly non-trivial - as a result [HS16]
was only able to treat part of the subcritical regime. Moreover, the cumulants
of these noises fall out of the scope of the later work [CH16]. In this work we
systematically leverage "charge" cancellations specific to this model and
obtain stochastic estimates that allow us to cover the entire subcritical
regime.
