[Paper Review] Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases

Thomas T. Dumitrescu, Po-Shen Hsin|arXiv (Cornell University)|Dec 28, 2023

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper proposes that Higgs and confinement phases in QCD can be distinguished by symmetry protected topological (SPT) order, leading to phase transitions when global symmetries—particularly time-reversal and parity—protect non-trivial theta-angles. By adding Higgs fields and Yukawa couplings to QCD, the authors show that confining phases are trivial SPTs, while Higgs phases exhibit non-trivial θf=π or θg=π, making them topological insulators/superconductors. At high baryon density, three-flavor QCD becomes a gapless SPT with θg=π, implying anomalous surface modes in neutron stars.

ABSTRACT

In gauge theories with fundamental matter there is typically no sharp way to distinguish confining and Higgs regimes, e.g. using generalized global symmetries acting on loop order parameters. It is standard lore that these two regimes are continuously connected, as has been explicitly demonstrated in certain lattice and continuum models. We point out that Higgsing and confinement sometimes lead to distinct symmetry protected topological (SPT) phases -- necessarily separated by a phase transition -- for ordinary global symmetries. We present explicit examples in 3+1 dimensions, obtained by adding elementary Higgs fields and Yukawa couplings to QCD while preserving parity P and time reversal T. In a suitable scheme, the confining phases of these theories are trivial SPTs, while their Higgs phases are characterized by non-trivial P- and T-invariant theta-angles $θ_f, θ_g = π$ for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional three-flavor QCD (without elementary Higgs fields) at finite $U(1)_B$ baryon-number chemical potential $μ_B$, which preserves P and T. At very large $μ_B$, three-flavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks $U(1)_B$. We argue that this high-density phase is in fact a gapless SPT, with a gravitational theta-angle $θ_g = π$ that safely co-exists with the $U(1)_B$ Nambu-Goldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quark-matter cores inside neutron stars.

Motivation & Objective

• To resolve the ambiguity in distinguishing Higgs and confinement phases in QCD using conventional order parameters.
• To establish that Higgs and confinement phases can be separated by a topological phase transition when protected by global symmetries like time-reversal and parity.
• To demonstrate that high-density three-flavor QCD is a gapless SPT with gravitational theta-angle θg=π, despite spontaneous U(1)B breaking.
• To explore the physical consequences of SPT order in neutron star interiors, particularly anomalous surface modes at phase boundaries.

Proposed method

• Constructing 3+1D gauge theories by adding elementary Higgs fields and Yukawa couplings to QCD while preserving P and T symmetry.
• Analyzing the resulting phases via generalized global symmetries and one-form symmetries acting on Wilson and 't Hooft loops.
• Using the dynamical response of the system to background gauge fields to identify non-trivial SPT phases via θf=π and θg=π.
• Applying the framework of anomaly inflow and boundary anomaly matching to show that a θg jump implies anomalous surface modes on domain walls.
• Deforming the high-density QCD phase to a zero-density Higgs-Yukawa-QCD model to infer the SPT nature of the high-μB phase.
• Computing the thermal Hall conductance on domain walls to detect non-trivial SPT order, with κxy = 1/4 + n/2 for n ∈ ℤ.

Experimental results

Research questions

• RQ1 Can Higgs and confinement phases in QCD be distinguished by topological order protected by global symmetries?
• RQ2 Under what conditions do Higgs and confinement phases become separated by a phase transition rather than being continuously connected?
• RQ3 Does high-density three-flavor QCD exhibit non-trivial SPT order, and if so, what is its topological invariant?
• RQ4 Can a gravitational theta-angle jump θg=π coexist with a Nambu-Goldstone boson in a gapless SPT phase?
• RQ5 What are the observable consequences of SPT order at the boundary of quark matter in neutron stars?

Key findings

• Higgs and confinement phases in QCD with added Higgs fields and Yukawa couplings are separated by a topological phase transition when protected by P and T symmetries.
• The confining phase is a trivial SPT, while the Higgs phase is a non-trivial SPT characterized by θf=π or θg=π, making it a topological insulator or superconductor.
• At high baryon density, three-flavor QCD is a gapless SPT with θg=π, even though it breaks U(1)B and hosts a Nambu-Goldstone boson.
• A jump in the gravitational theta-angle Δθg=π across a domain wall leads to a non-trivial thermal Hall conductance κxy = 1/4 + n/2, indicating anomalous surface modes.
• The presence of θg=π in neutron star quark cores implies the existence of anomalous surface modes, potentially observable via thermal transport.
• The SPT nature of the high-density phase implies unexpected phase transitions in the QCD phase diagram, distinct from the U(1)B-breaking superfluid transition.