Yes, there are several proposed theories that discuss physical processes occurring in higher dimensions beyond the familiar three dimensions of space and one dimension of time. These theories are usually motivated by attempts to unify fundamental forces, explain the properties of particles, or provide a framework for understanding phenomena like gravity.
One prominent example is string theory, which suggests that fundamental particles are not point-like objects but rather tiny strings vibrating in higher-dimensional space. String theory requires extra dimensions—typically, 10 or 11 dimensions—to be consistent mathematically. These extra dimensions are often compactified or curled up into tiny, unobservable scales.
Another proposal is the braneworld scenario, which suggests that our observable universe is a 3-dimensional "brane" embedded in a higher-dimensional space called the bulk. In this theory, gravity can propagate in the higher-dimensional bulk, while other forces are confined to the brane. This idea has been explored in models such as the Randall-Sundrum model.
Supersymmetry, a theoretical framework that extends the Standard Model of particle physics, also introduces extra dimensions. In supersymmetry, each known particle has a superpartner particle with different spin, and these superpartners could reside in higher-dimensional space.
Furthermore, some variations of quantum gravity theories, such as loop quantum gravity and causal dynamical triangulation, propose that spacetime is fundamentally discrete at the smallest scales, and these discrete structures may exist in higher dimensions.
It's important to note that these proposed theories involving higher dimensions are still subjects of active research and do not have definitive experimental confirmation. They are theoretical frameworks that aim to address various problems in fundamental physics and may potentially provide a deeper understanding of the universe.