The Discrete Gaussian Free Field (DGFF) has a straightforward interpretation as a field theory, where local fields are just polynomials on (the gradient of) the field itself. Guided by the constructions (in the continuum) of Conformal Field Theory (CFT), the space of local fields of the DGFF can be rendered a Virasoro representation. From there, and yet again following the CFT intuition, the scaling limit (and the renormalisation exponents for it to exist) of correlations of such observables can be computed and checked to be given by correlation functions of the corresponding local fields in the free boson CFT.
This is joint work with D. Behzad and K. Kytölä.
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