- The paper identifies the controversial contact term in Maxwell theory as the entanglement entropy of electromagnetic edge modes.
- It employs heat kernel regularization and a lattice-like physical regulator to resolve divergences and integrate classical electric field fluctuations into a coherent statistical framework.
- The approach connects Maxwell theory's entanglement entropy with black hole thermodynamics, gauge-gravity duality, and confinement, offering insights for both quantum field theory and condensed matter applications.
Entanglement Entropy of Electromagnetic Edge Modes
This paper examines the long-standing issue in the entanglement entropy analysis of Maxwell theory by addressing a puzzling term devoid of a relevant statistical interpretation. The authors resolve this through their analysis of electromagnetic edge modes, attributing to these edge modes the unexpected term in question.
The paper focuses on the Maxwell theory's vacuum entanglement entropy and the regularization of divergences which have troubled researchers over the years. Traditionally, entanglement entropy calculations using Euclidean methods exhibit an area-law divergence akin to that expected for scalar fields. However, a non-trivial "contact term," variable based on the calculation method, has sparked debate regarding its interpretation and significance.
The novel insight provided by Donnelly and Wall involves interpreting this contact term as the entanglement entropy associated with edge modes: specifically, classical solutions influenced by the electric field along the entangling surface. By utilizing a heat kernel regularization, the researchers identify a negative divergence, previously noted by Kabat, tracing it back as a manifestation of the edge modes' entanglement entropy.
Important results stem from the convergence of their approach with prior entanglement entropy studies on black hole thermodynamics, gauge-gravity duality, and confinement. This work directly connects the geometric entropy of gauge fields and logarithmic divergences with statistical constructs, notably resolving discrepancies connected to the entanglement entropy and corresponding conformal anomaly in 3+1 dimensions.
By employing a physical regulator analogous to a lattice and incorporating boundary flux modifications, the researchers articulate a sum over edge modes at the boundary rather than boundary condition constraints. This formulation allows for the integration of classical electric field fluctuations into a coherent statistical entropy framework, contributing to a comprehensive understanding of entropy in gauge fields.
Implications of this research extend to both theoretical and practical applications. Theoretically, the paper provides a robust resolution for entropic terms in quantum field theories, suggesting further exploration into diverse regulator schemes and their impacts on entropy calculations in quantum gravity contexts. Practically, applications in condensed matter physics and confinement theories could benefit from the underlying mathematical structures elucidated herein.
The analyses conducted by Donnelly and Wall open avenues for future exploration on topics such as the distinction between lattice gauge theories and classical field theories in the continuum limit and the potential influence of edge modes within other gauge theories beyond electromagnetism, including non-Abelian fields and gravity. These edge considerations illuminate potential avenues for reconciling discrepancies in asymptotic spaces, especially within the framing of quantum gravity theories seeking UV completion through mechanisms like asymptotic safety.
In summary, this paper represents a methodical examination of Maxwell theory, elucidating previously confounding terms through comprehensive treatment of edge modes. The findings present a structured way forward in addressing divergences in entanglement entropy calculations, with broad implications across various fields of theoretical physics.