Electromagnetic Duality and Entanglement Anomalies

Abstract

Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of freedom rearranged in a nonlocal fashion. We study this phenomenon in the context of the electromagnetic duality of abelian $p$-forms. A careful calculation of the duality anomaly on an arbitrary $D$-dimensional manifold shows that the effective actions agree exactly in odd $D$, while in even $D$ they differ by a term proportional to the Euler number. Despite this anomaly, the trace of the stress tensor agrees between the dual theories. We also compute the change in the vacuum entanglement entropy under duality, relating this entanglement anomaly to the duality of an "edge mode" theory in two fewer dimensions. Previous work on this subject has led to conflicting results; we explain and resolve these discrepancies.

16 pages + appendices

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Cited by in corpus (15)

• Electromagnetic duality and central charge
• Dynamical Edge Modes and Entanglement in Maxwell Theory
• Fermionization of conformal boundary states
• On the logarithmic coefficient of the entanglement entropy of a Maxwell field
• Comments on Defining Entanglement Entropy
• Weyl, Pontryagin, Euler, Eguchi and Freund
• Ryu-Takayanagi Area as an Entanglement Edge Term
• Superselection Sectors of Gravitational Subregions
• Entanglement entropy, dualities, and deconfinement in gauge theories
• Odd dimensional analogue of the Euler characteristic
• Dynamical Edge Modes in $p$-form Gauge Theories
• Entanglement entropy and non-local duality: quantum channels and quantum algebras
• Duality Anomalies in Linearized Gravity
• Aspects of Higher-Abelian Gauge Theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops
• Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday