Abstract
We demonstrate that the near horizon symmetries of black holes in Einstein-Yang-Mills (EYM) theory are generated by an infinite-dimensional algebra that contains, in addition to supertranslations and superrotations, a non-Abelian loop algebra. This means that the Virasoro-Kac-Moody structure of EYM in asymptotically flat spacetimes has an exact analog in the near horizon region.
Highlights
In 2015, Hawking conjectured that, in their near horizon limit, black holes might exhibit an infinite-dimensional symmetry [1] similar to the supertranslations that appear near null infinity in asymptotically flat spacetimes [2–4]
The study of infinite-dimensional symmetries in the near horizon region has antecedents [13–15], and more recently it led to interesting developments and generalizations; see for instance [16–25]
We will consider the case of Einstein gravity coupled to Yang-Mills theory for an arbitrary gauge group G, and we will show that, in addition to supertranslations and superrotations, the black holes of the theory exhibit an infinite-dimensional symmetry that is generated by a nonAbelian loop algebra. This means that, as it happens in Einstein-Yang-Mills theory in asymptotically flat spacetimes [26], a Virasoro-Kac-Moody structure emerges in the near horizon region of colored black holes
Summary
In 2015, Hawking conjectured that, in their near horizon limit, black holes might exhibit an infinite-dimensional symmetry [1] similar to the supertranslations that appear near null infinity in asymptotically flat spacetimes [2–4]. We will consider the case of Einstein gravity coupled to Yang-Mills theory for an arbitrary gauge group G, and we will show that, in addition to supertranslations and superrotations, the black holes of the theory exhibit an infinite-dimensional symmetry that is generated by a nonAbelian loop algebra. This means that, as it happens in Einstein-Yang-Mills theory in asymptotically flat spacetimes [26], a Virasoro-Kac-Moody structure emerges in the near horizon region of colored black holes.
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