  Optical trapping is an indispensable tool in physics and the life sciences.
However, there is a clear trade off between the size of a particle to be
trapped, its spatial confinement, and the intensities required. This is due to
the decrease in optical response of smaller particles and the diffraction limit
that governs the spatial variation of optical fields. It is thus highly
desirable to find techniques that surpass these bounds. Recently, a number of
experiments using nanophotonic cavities have observed a qualitatively different
trapping mechanism described as "self-induced back-action trapping" (SIBA). In
these systems, the particle motion couples to the resonance frequency of the
cavity, which results in a strong interplay between the intra-cavity field
intensity and the forces exerted. Here, we provide a theoretical description
that for the first time captures the remarkable range of consequences. In
particular, we show that SIBA can be exploited to yield dynamic reshaping of
trap potentials, strongly sub-wavelength trap features, and significant
reduction of intensities seen by the particle, which should have important
implications for future trapping technologies
