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I will give a lightening review of the theory of classical background fields induced by the Becchi-Rouet-Stora-Tyutin algebra of a spinning particle, such as the graviton. On a generic background, the closure of the algebra implies Einstein’s equations with a cosmological constant that is undetermined. In the "vacuum" background without any metric, elementary excitations consist of a bunch of non-dynamical scalar- and vector fields. However, only certain combinations of these, survive beyond the linear level with the vector field inducing an Einstein metric.