Abstract
Gravitational instantons with NUT charge are magnetic monopoles upon dimensional reduction. We determine whether NUT charge can proliferate via the Polyakov mechanism and partially screen gravitational interactions. In semiclassical Einstein gravity, Taub-NUT instantons experience a universal attractive force in the path integral that prevents proliferation. This attraction further leads to semiclassical clumping instabilities, similar to the known instabilities of hot flat space and the Kaluza-Klein vacuum. Beyond pure Einstein gravity, NUT proliferation depends on the following question: is the mass of a gravitational instanton in the theory always greater than its NUT charge? Using spinorial methods we show that the answer to this question is `yes' if all matter fields obey a natural Euclidean energy condition. Therefore, the attractive force between instantons in the path integral wins out and gravity is dynamically protected against screening. Semiclassical gravity with a compactified circle can be self-consistently quantum ordered, at the cost of suffering from clumping instabilities.
Highlights
Charge was raised by Gross in [11], but does not appear to have been further discussed.1 Some of the discussion in that paper anticipates our concerns in this work
Beyond pure Einstein gravity, NUT proliferation depends on the following question: is the mass of a gravitational instanton in the theory always greater than its NUT charge? Using spinorial methods we show that the answer to this question is ‘yes’ if all matter fields obey a natural Euclidean energy condition
We show that if the matter fields obey a natural Euclidean local energy condition, the mass of a gravitational instanton is greater than its NUT charge
Summary
We quickly review Polyakov’s computation [9, 25] in order to establish notation and concepts that we will use below. If the separation between the instantons is parametrically larger than the core size, for the purposes of determining the interaction, the core may be replaced by a delta function source for the magnetic field. A multi-instanton configuration will be characterized by a fixed number of delta functions sources and we do the path integral over the magnetic field subject to the presence of sources. The proliferation of a magnetically charged instanton gas in the path integral has Debye screened the (dualized) Maxwell field. The upshot of this discussion is that the proliferation of topologically nontrivial field configurations in the path integral has gapped the would-be massless gauge field. For a discussions of fermions and monopole proliferation very much in the spirit of the present paper see [15, 16]
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