Hilbert series, the Higgs mechanism, and HEFT

A bstract We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, enumeration operator bases non-linearly realized gauge theories. find that Higgs mechanism is manifest at level series, as expected partition function an S -matrix subject to Goldstone equivalence theorem. In addition vectors, we detail how massive, spinning particles can be studied with series; particular, spell out ingredients gravity general spacetime dimensions. Further methodology introduced enable capture effect spurion fields acquiring vevs. apply techniques Effective Field Theory (HEFT), providing a systematic its basis. This achieved both from direct and custodial symmetry spurion-based approach; compare contrast two approaches, our results those appearing previous literature.