Bosonization in Higher Dimensions

Abstract

Bosonization is a beautiful phenomena which maps fermions to bosons. In 2D the existence of bosonization is well studied. In 3D however existence of anyons provide us an indirect route to bosonization. A microscopic theory which realises this is the Chern-Simons matter theory. In this thesis we study bosonization in 3D by considering Chern-Simons matter theories. These theories possess an extra higher spin symmetry which can be exploited to constrain the correlation functions. We study their anyonic behaviour by using higher spin symmetry which allows us to map the interacting theory correlators to their free theory counterparts. We explicitly show that the anyonic nature arises at the level of two-point, three-point and four-point correlators and how this anyonic nature provides a way towards bosonization.