Loop quantum gravity is a perspective candidate for the quantum theory of gravity. However, there is a conceptual controversy in it: having started from the Einstein-Hilbert action and describing spacetime without matter, we can hardly define spacetime as anything other than a set of relations between matter fields. Here, following the Penrose idea of combinatorial spacetime we reformulate loop quantum gravity theory solely in terms of the matter fields.
M. V. Altaisky (Sun,) studied this question.