It seems that a few higher dimensional theories exist, but they are not very well understood.

For a 10 dimensional supersymmetric theory we are allowed a 32-component Majorana spinor.

To investigate three dimensions starting from the four dimensional theory should be possible, because the intersection probabilities of random walks depend continuously on the dimensionality of the space.

These suggest a universal behavior of the superconducting phase transition, by describing phase transitions as field theories on the boundary of a higher dimensional gravitational theory.

Initially a two dimensional theory of knowledge creation was proposed (Nonaka 1994: 16-17; Nonaka & Takeuchi 1995: 57-60).

Robert Plutchik offers a three-dimensional model that is a hybrid of both basic-complex categories and dimensional theories.

The finite dimensional theory is greatly governed by a theory of root systems and Dynkin diagrams, strikingly similar to those of semisimple Lie algebras.

This was the first of the extra dimensional theories, which later came to be known as Kaluza-Klein theory.

This was later increased to 11 dimensions based on various interpretations of the ten dimensional theory that led to five partial theories as described below.

N.B. : Here, a symmetry is said to be local or global from the two dimensional theory (on the worldsheet) point of view.