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Some of the exciting phenomena uncovered in strongly correlated systems inrecent years - for instance quantum topological order, deconfined quantumcriticality, and emergent gauge symmetries -- appear in systems in which theHilbert space is effectively projected at low energies in a way that imposeslocal constraints on the original degrees of freedom. Cases in point includespin liquids, valence bond systems, dimer models, and vertex models. In thiswork, we use a slave boson description coupled to a large-$S$ path integralformulation to devise a generalised route to obtain effective field theoriesfor such systems. We demonstrate the validity and capability of our approach bystudying quantum dimer models and by comparing our results with the existingliterature. Field-theoretic approaches to date are limited to bipartitelattices, they depend on a gauge-symmetric understanding of the constraint, andthey lack generic quantitative predictive power for the coefficients of theterms that appear in the Lagrangians of these systems. Our method overcomes allthese shortcomings and we show how the results up to quadratic order comparewith the known height description of the square lattice quantum dimer model, aswell as with the numerical estimate of the speed of light of the photonexcitations on the diamond lattice. Finally, instanton considerations allow usto infer properties of the finite-temperature behaviour in two dimensions.

Generalised route to effective field theories for quantum systems with local constraints