Quantum distillation in QCD

Abstract

We propose a grading protocol which assigns global symmetry associated phases to states in the Hilbert space. Without modifying the Hilbert space, this changes the state sum, a process that we call quantum distillation. We describe the image of quantum distillation in path integral in terms of (non-dynamical) flavor holonomy dependence of (dynamical) gauge holonomy potentials, in QCD with $N_f=N_c$ fundamental and one massive adjoint fermion on ${\mathbb{R}}^3\times S^1$. The compactified theory possesses an exact zero-form color-flavor center symmetry for a special choice of flavor holonomy (under which Polyakov loop is charged), despite the absence of one-form center-symmetry. We prove that the CFC symmetry is stable at small-$\beta$. This is the opposite of the high-temperature limit of thermal theory and a dramatic manifestation of quantum distillation. We show chiral symmetry breaking at small $S^1$ and that the vacuum structure of the theory on ${\mathbb{R}}^4$ and ${\mathbb{R}}^3\times S^1$ are controlled by the same mixed 't Hooft anomaly condition.

7 pages

References in corpus (10)

• Generalized Global Symmetries
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Volume independence in large Nc QCD-like gauge theories
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Circle compactification and 't Hooft anomaly
• Order parameters and color-flavor center symmetry in QCD
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Two-loop perturbative corrections to the constrained effective potential in thermal QCD
• Bose-Fermi cancellations without supersymmetry
• Volume independence for Yang-Mills fields on the twisted torus

Cited by in corpus (8)

• On the baryon-color-flavor (BCF) anomaly in vector-like theories
• Lifetimes of (near) eternal false vacua
• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Lattice simulations of a gauge theory with mixed adjoint-fundamental matter
• Exploring gauge theories with adjoint matter on the lattice
• Consistency of $\chi$SB in chiral Yang-Mills theory with adiabatic continuity
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD