Emergent dimensions and quantum critical points

When quantum many-body systems are strongly correlated, the underlying particles may dynamically organize themselves to show novel collective behaviors. Under certain conditions, collective fluctuations behave as if they are living in a space which has one more dimension than the space where the original particles are defined. In this talk, I will discuss about an example where an `external' space emerges at a quantum critical point of a non-abelian gauge theory. A close analogy will be drawn between this phenomenon and fractionalization which can be viewed as an example of emergent `internal' spaces. I will also discuss about non-trivial quantum orders associated with emergent dimensions.