Schwinger-Dyson equation for connected correlation functions

Could someone tell me what’s the Schwinger-Dyson equation for connected correlation functions? I’m looking for a formula that relates a connected $n+1$-point function to connected lower point functions.

More specifically, I’m reading this article by Dijkgraaf and Vafa, https://arxiv.org/abs/0711.1932, and I’m trying to understand sections 3.1 and 3.3. There they consider the action $$S = int_Sigma left[frac{1}{2}partial beta overline{partial}beta + beta overline{partial}gammaright] + int_{partial Sigma} left[frac{omega}{lambda} beta + beta gamma + frac{lambda}{omega} beta gamma^2right]$$
with $lambda$ a small coupling constant, and with propagators
$$
langle beta(z)beta(z’) rangle =0 langle beta(z)gamma(z’) rangle = G(z,z’) langle gamma(z)gamma(z’) rangle =B(z,z’)
$$
and then they schematically derive a recursion relation for connected correlation functions $langle gamma(z_1) dots gamma(z_n)rangle_{conn}$, presumably from the Schwinger-Dyson equations or some version of Wick’s theorem. How do I figure out what the relevant S-D equation is, and how to find the corresponding boundary conditions, from the above action?