We consider a deformation of N = 1 supersymmetric
gauge theories in four dimensions, which we call the C-deformation,
where the gluino field satisfies
a Clifford-like algebra dictated by a self-dual two-form,
instead of the standard Grassmannian algebra. The superpotential
of the deformed gauge theory is computed by the full partition
function of an associated matrix model (or more generally
a bosonic gauge theory), including non-planar diagrams. In
this identification, the strength of the two-form controls
the genus expansion of the matrix model partition function.
For the case of pure N = 1 Yang-Mills this deformation
leads to the identification of the all genus partition function of c non-critical bosonic
string at self-dual radius
as the glueball superpotential.
Though the C-deformation violates Lorentz invariance,
the deformed F-terms are Lorentz invariant and
the Lorentz violation is screened in the IR.