Entanglement Monotonicity and the Stability of Gauge Theories in Three Spacetime Dimensions

We employ the recent results on the generalization of the central charge theorem to three spacetime dimensions to derive nonperturbative results for several strongly interacting quantum field theories, including quantum electrodynamics (QED-3), and the theory corresponding to certain quantum phase transitions in condensed matter systems. In particular, by demanding that the universal constant part of the entanglement entropy decreases along the renormalization group flow ($F$ theorem), we find sufficient conditions for the stability of QED-3 against chiral symmetry breaking and confinement. Using similar ideas, we derive strong constraints on the nature of quantum critical points in condensed matter systems with topological order.

Figure 1

A RG flow that is prohibited due to the $F$ theorem. Gaussian, W-F, Goldstone, and TQFT refer, respectively, to the Gaussian fixed point, the Wilson-Fisher fixed point, a Goldstone mode phase, and an arbitrary topologically order phase of an SU(2) symmetric spin system in $(2+1)\mathrm{D}$.