The higher order topological insulators (HOTIs) are a good playground to ask questions on spatial dimensionality in general physics. String theory, as a consistent quantum gravity, has a peculiar ability to control spacetime dimensions to accommodate various physics systems. In 2016, we eventually discovered the notion of continuum HOTI, independently from the major work by Benalcazar et al., where our findings were naturally derived by applying the ideas of solitons, duality, and branes, which are major ingredients used in string theory, to topological materials. This talk explains our path, and discusses the physical origin of the continuum HOTIs from such string-theoretic or field-theoretic viewpoints.

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