Topological characterization of higher-dimensional charged Taub–NUT instantons

Abstract

Topological excitations of gauge fields exhibit a discrete behavior, which arises from the global structure. We calculate the Chern numbers of higher dimensional Taub-NUT and Taub-Bolt instantons and find the winding numbers, which classify the U(1)−bundles that harbor Maxwell dyons. Our results can be written in general for any even dimension and apply for many different theories of gravity. We illustrate this point by focusing on Lovelock gravity. The magnetic flux is found to be a pure topological excitation whereas the electric flux is indirectly indexed by the magnetic counterpart. We argue that this last result is a consequence of the path integral approach to quantum gravity.MSC: 32L81, 51P05, 55R15, 58J28, 81T70

Nonlinear extensions of gravitating dyons: from NUT wormholes to Taub-Bolt instantons

“…(3.22) and(3.23) we see that the Euclidean ModMax configuration is asymptotically Maxwell. This is to say, the results of refs [87,88]. apply…”

“…This is a general phenomenon for selfdual Euclidean Maxwell JHEP09(2021)104 fields; see for example [86] and references therein. For Taub-NUT spaces there is also a relation between selfduality, or the lack thereof, and topological charge [87]. Because of the topological nature of this result, it also holds for nonlinear electrodynamics; see e.g.…”

Charged Taub-NUT solution in Lovelock gravity with generalized Wheeler polynomials

“…The warping functions in the Wheeler polynomial are independent of the rescalings of the base manifold, except in the coefficients which encode its geometry. The Taub-Bolt branch of the solution presented here, is a generalization of the Dirac monopole which includes self-gravity [41]. It has a unique Chern index [cf.…”

Pure Gauss-Bonnet NUT Black Hole Solution: I

“…The presence of NUT charge in higher dimensional black hole solutions introduces a topological impediment, which we have found to be true for both Einstein and Gauss-Bonnet gravity. Due to this limitation, there exists no higher dimensional NUT black hole with spherical topology, however, they do exist with non-spherical product topology [44,45]. But there is no discussion about why spherical topology is not allowed?…”