Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity

We employ the recent results on the generalization of the $c$-theorem to 2+1-d to derive non-perturbative results for strongly interacting quantum field theories, including QED-3 and the critical 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 bounds on the number of flavors of fermions required for the stability of QED-3 against chiral symmetry breaking and confinement. In this context, the exact results known for the entanglement of superconformal field theories turn out to be quite useful. Furthermore, the universal number corresponding to the ratio of the entanglement entropy of a free Dirac fermion to that of free scalar plays an interesting role in the bounds derived. Using similar ideas, we also derive strong constraints on the nature of quantum critical points in condensed matter systems with "topological order".