Gravitational Solitons and Completeness
Jacob McNamara
TL;DR
The paper argues that the presence of gravitational solitons—topology-enabled excitations—introduces gauge charges beyond those of local fields and, crucially, breaks non-invertible 1-form symmetries down to a group-like sub-symmetry. This leads to a streamlined path to the Completeness Hypothesis: once these solitons are accounted for, completeness follows from the remaining symmetry being broken, especially when additional matter further breaks any residual symmetry. The authors formalize charges via braided semisimple tensor categories, identifying the gravitational soliton charges with the adjoint subcategory, and extend the analysis to higher branes using higher-category theory. They illustrate the general mechanism with concrete examples, including discrete holonomies and vortices, and discuss implications for the Swampland program, cobordism, and potential connections to lattice systems. Overall, the work provides a gravity-centered, categorical framework in which completeness arises naturally from topology fluctuations and symmetry-breaking.
Abstract
We show that gravitational solitons naturally carry gauge charges beyond those of any local quantum field. The effect of these charged excitations is to break a non-invertible symmetry to its maximal group-like sub-symmetry. Taking these charges into account, we show that the Completeness Hypothesis follows from the breaking of the remaining group-like symmetry. We generalize this picture to an arbitrary semisimple tensor category of particle charges, showing that the charges of gravitational solitons form the adjoint subcategory. We discuss a further generalization involving the charges of extended objects.