Comments on Charges and Near-Horizon Data of Black Rings
Kentaro Hanaki, Keisuke Ohashi, Yuji Tachikawa
TL;DR
The paper develops a horizon-centered framework to extract asymptotic charges of five-dimensional black rings with Chern-Simons terms, using Page charges and a two-patch gauge formalism to handle A∧F topological contributions. It demonstrates that angular momenta and electric charges can be computed entirely from near-horizon data and that these horizon charges correspond to four-dimensional charges after Kaluza-Klein reduction, with large gauge transformations mapping to the Witten effect on dyons and inducing monodromies. The results establish explicit mappings between 5d Page/Noether charges and 4d charges, clarifying how dipole and nut charges influence the 4d attractor mechanism and the moduli z^I, and provide a consistent route to incorporate higher-derivative corrections and multi-ring configurations. Overall, the work unifies the near-horizon encoding of charges with 4d/5d duality, enabling horizon-derived predictions for entropy corrections and attractor data in multi-ring systems.
Abstract
We study how the charges of the black rings measured at the asymptotic infinity are encoded in the near-horizon metric and gauge potentials, independent of the detailed structure of the connecting region. Our analysis clarifies how different sets of four-dimensional charges can be assigned to a single five-dimensional object under the Kaluza-Klein reduction. Possible choices are related by the Witten effect on dyons and by the large gauge transformation in four and five dimensions, respectively.