[Paper Review] Gauge-independent transition dividing the confinement phase in the lattice SU(2) gauge-adjoint scalar model

Akihiro Shibata, Kei-Ichi Kondo|arXiv (Cornell University)|Jul 29, 2023

Particle physics theoretical and experimental studiesPhysics and Astronomy3 citations

TL;DR

This study re-examines the phase structure of the lattice SU(2) gauge-adjoint scalar model using a gauge-independent approach, avoiding gauge fixing by employing the gauge-covariant CDGSFN decomposition. It confirms the known Higgs-confinement transition and discovers a new transition line that splits the conventional confinement phase into two distinct subphases, suggesting a deeper mechanism for confinement beyond standard Higgs or dual superconductor pictures.

ABSTRACT

The lattice SU(2) gauge-scalar model with the scalar field in the adjoint representation of the gauge group has two completely separated confinement and Higgs phases according to the preceding studies based on numerical simulations which have been performed in the specific gauge fixing based on the conventional understanding of the Brout-Englert-Higgs mechanism. In this paper, we re-examine this phase structure in the gauge-independent way based on the numerical simulations performed without any gauge fixing. This is motivated to confirm the recently proposed gauge-independent Brout-Englert-Higgs mechanism for generating the mass of the gauge field without relying on any spontaneous symmetry breaking. For this purpose we investigate correlation functions between gauge-invariant operators obtained by combining the original adjoint scalar field and the new field called the color-direction field which is constructed from the gauge field based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. Consequently, we reproduce gauge-independently the transition line separating confinement phase and Higgs phase, and show surprisingly the existence of a new transition line that divides completely the confinement phase into two parts. Finally, we discuss the physical meaning of the new transition and implications to confinement mechanism.

Motivation & Objective

• To investigate the phase structure of the SU(2) gauge-adjoint scalar model in a gauge-invariant manner, avoiding reliance on gauge fixing.
• To test the recently proposed gauge-independent Brout-Englert-Higgs (BEH) mechanism for generating gauge boson mass without spontaneous symmetry breaking.
• To determine whether the conventional separation between confinement and Higgs phases is robust under gauge-invariant analysis.
• To explore the physical origin of confinement by identifying new phase transitions within the confinement phase.
• To examine the role of the color-direction field and gauge-invariant composite operators in characterizing distinct phases.

Proposed method

• Utilizes the gauge-covariant CDGSFN decomposition of the gauge field to extract the color-direction field from the gauge field configuration.
• Constructs gauge-invariant composite operators from the adjoint scalar field and the color-direction field to probe phase structure.
• Performs numerical simulations on the lattice without any gauge fixing, preserving full gauge invariance.
• Measures correlation functions between gauge-invariant operators to identify phase transitions.
• Analyzes the vacuum expectation value of the gauge-invariant operator Q = n·φ to detect alignment between scalar and color-direction fields.
• Compares results with previous gauge-fixed studies to confirm consistency and detect new features.

Experimental results

Research questions

• RQ1 Does the Higgs-confinement phase transition persist in a gauge-independent formulation of the SU(2) gauge-adjoint scalar model?
• RQ2 Can a new phase transition be identified within the conventional confinement phase using gauge-invariant observables?
• RQ3 What is the physical origin of the newly discovered phase transition, and how does it differ from the standard confinement and Higgs phases?
• RQ4 How does the gauge-independent BEH mechanism manifest in the phase structure, particularly in the absence of spontaneous symmetry breaking?
• RQ5 Is the new phase structure a lattice artifact or does it survive the continuum limit?

Key findings

• The gauge-independent analysis successfully reproduces the known transition line separating the Higgs phase from the confinement phase, confirming consistency with previous gauge-fixed studies.
• A new transition line is discovered that completely divides the conventional confinement phase into two distinct subphases, labeled (I) and (III).
• In phase (I), magnetic monopoles arise primarily from the gauge field degrees of freedom, consistent with the dual superconductor picture.
• In phase (III), magnetic monopoles are mainly sourced by the adjoint scalar field, resembling the 't Hooft-Polyakov monopole in the Georgi-Glashow model.
• The vacuum expectation value ⟨Q⟩ = ⟨n·φ⟩ > 0 in the region γ > γc(β), indicating alignment between the color-direction field and the scalar field, signaling a distinct phase.
• The new phase (III) is characterized by massive gauge fields due to self-interactions, with no evidence of spontaneous gauge symmetry breaking, supporting the gauge-independent BEH mechanism.