Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching

Understand

A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space.

• An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the state-sum, without affecting the ground states; we call this effect "quantum distillation".
• Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under $S^1$ compactification.
• We revisit this point via the 't Hooft anomaly matching condition when it constrains the vacuum structure of the theory on $\mathbb{R}^d$ and upon compactification.