Gravity from Symmetry Breaking Phase Transition

The paper is devoted to the memory of Dmitry Diakonov. We discuss gravity emerging in the fermionic vacuum as suggested by Diakonov 10 years ago in his paper "Towards lattice-regularized Quantum Gravity". [1] Gravity emerges in the phase transition. The order parameter in this transition is the tetrad field $e_{\mu }^a$ , which appears as the bilinear composite of the fermionic fields. The similar scenario of the symmetry breaking takes place in the B-phase of superfluid ${}^3$ He, where the real part of the spin-triplet p-wave order parameter matrix $A_{\mathrm{ai}}$ plays the role of the emerging tetrad (triad). In Diakonov theory this symmetry breaking gives 6 Nambu-Goldstone modes; 6 gauge bosons in the spin-connection fields, which absorb 6 NG modes and become massive gauge bosons; and 6 Higgs fields. In ${}^3$ He-B, these Higgs collective modes correspond to 6 massive gravitons, while in the emerging general relativity the Higgs collective modes give rise to two massless gravitational waves.