Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity

TL;DR

This paper leverages the 2+1-d entanglement monotonicity (the F-theorem) to obtain non-perturbative bounds on strongly coupled gauge theories, notably QED-3 and its supersymmetric deformation, with implications for chiral symmetry breaking and deconfinement. By comparing UV and IR entanglement contributions and employing a deformation from $ ext{N}=2$ SQED-3 to non-SUSY QED-3, it derives a rigorous bound $N_{f, ext{CSB}}<7$ and shows deconfinement in compact QED-3 for $N_f>6$. The analysis also constrains the nature of quantum critical points, ruling out certain transitions to topologically ordered phases from lying in conventional $O(N)$ universality classes, and highlighting Ising$^*$-type transitions. These results provide non-perturbative constraints on the phase structure of 2+1-d gauge theories and their condensed-matter realizations, with broad implications for spin liquids and deconfined quantum criticality.

Abstract

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".

Figures (1)

• Figure 1: An RG flow that is prohibited due to entanglement monotonicity/F-theorem. The Gaussian fixed point has $\gamma = 3 \times \gamma_{scalar} \approx 0.18$ while the topological ordered phase has $\gamma$ that equals the topological entanglement entropy and is bigger and satisfies $\gamma > \log(\sqrt{2}) \approx 0.35$. This means that the quantum phase transition separating the topological ordered phase and the antiferromagnet cannot be $O(3)$ critical, on general grounds. Similar arguments can be made for several other quantum critical points in condensed matter systems (see the main text).