Entanglement entropy of electromagnetic edge modes.

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• Entanglement Entropy

Background:

• Standard calculations of vacuum entanglement entropy in Maxwell theory yield an unexplained term.
• This anomaly has persisted for two decades without a clear statistical interpretation.
• Recent studies highlighted logarithmic divergences in gauge fields, adding to the puzzle.

Purpose of the Study:

• To resolve the two-decade-old puzzle of the unexpected term in Maxwell theory's vacuum entanglement entropy.
• To provide a statistical interpretation for this anomalous term.
• To explain logarithmic divergences observed in gauge fields.

Main Methods:

• Identifying the anomalous term as the entanglement entropy of edge modes.
• Characterizing edge modes as classical solutions dictated by the electric field normal to the entangling surface.
• Applying heat kernel regularization to the entanglement entropy of edge modes.

Main Results:

• The unexpected term in vacuum entanglement entropy is attributed to the entanglement entropy of edge modes.
• Heat kernel regularization of this edge mode entropy reproduces Kabat's negative divergent expression.
• The calculation resolves puzzles related to logarithmic divergences in 3+1 dimensional gauge fields.

Conclusions:

• The statistical interpretation of vacuum entanglement entropy in Maxwell theory is now understood through edge modes.
• This work clarifies fundamental aspects of entanglement entropy in gauge theories.
• The findings have implications for understanding quantum field theory divergences and entropy calculations.