Abstract
We elucidate the mismatch between the $A$-anomaly coefficient and the coefficient of the logarithmic term in the entanglement entropy of a Maxwell field. In contrast to the usual assumptions about the protection of renormalization group charges at the infrared, the logarithmic term is different for a free Maxwell field and a Maxwell field interacting with heavy charges. This is possible because of the presence of superselection sectors in the IR theory. However, the correction due to the coupling with charged vacuum fluctuations, that restores the anomaly coefficient, is independent of the precise UV dynamics. The problem is invariant under electromagnetic duality, and the solution requires both the existence of electric charges and magnetic monopoles. We use a real-time operator approach but we also show how the results for the free and interacting fields are translated into an effective correction to the four-sphere partition function.
Highlights
Entanglement entropy (EE) is an unconventional and useful theoretical quantity in the exploration of quantum field theories (QFT). It has been especially important in connection with holographic theories and the understanding of the renormalization group (RG) irreversibility
We describe how the physical effect of heavy charges on the flux statistics across large surfaces described in the previous section is responsible for the change of the logarithmic coefficient of the entropy of a sphere
To see how the mutual information changes with ε in presence of charges, as we have discussed in Sec
Summary
Entanglement entropy (EE) is an unconventional and useful theoretical quantity in the exploration of quantum field theories (QFT). A related problem is how a correction that depends on the details of the UV, such as the one associated with the presence of massive charges, could affect the IR result universally This again is not restricted to the case of the Maxwell field and happens for other models with superselection sectors [15]. The last question is why the universal result for the interacting model numerically coincides with the anomaly
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