Thermofield Double States in Group Field Theory

Abstract

Group field theories are higher-rank generalizations of matrix/tensor models, and encode the simplicial geometries of quantum gravity. In this paper, we study the thermofield double states in group field theories. The starting point is the equilibrium Gibbs states in group field theory recently found by Kotecha and Oriti, based on which we construct the thermofield double state as a thermal vacuum respecting the Kubo-Martin-Schwinger condition. We work with the Weyl $C^*$-algebra of group fields, where the group fields and their Hermitian conjugations respectively annihilate and create quantum polyhedra in the sense of second quantization. A particular type of thermofield double states with single type of symmetry are then obtained from the squeezed states on this Weyl algebra. In particular, the ``tilde system is obtained from the original system via modular conjugations, and we interptret the ``tilde system as an emergent referencial system. The thermofield double states, when viewed as states on the group field theory Fock vacuum, are condensate states at finite flow parameter $\\beta$. We suggest that the equilibrium flow parameters $\\beta$ of this type of thermofield double states in the group field theory condensate pictures of black hole horizon and quantum cosmology are related to the inverse temperatures in gravitational thermodynamics.