#### Alladi Ramakrishnan Hall

#### Chern-Simons matter theories, Bose-Fermi duality and anyonic statistics

#### Naveen S. Prabhakar

##### ICTS, Bangalore

*Physics in two spatial dimensions is strange due to the possibility of*

the existence of anyons -- particle-like excitations which possess

arbitrary real spin, and arbitrary exchange statistics. In this talk,

we describe the coupling of scalar and fermionic degrees of freedom to

non-abelian Chern-Simons gauge theories and the signatures of anyonic

physics in the many quantities - partition functions, S-matrices,

occupation number distributions and so on - that have been exactly and

explicitly computed in the 't Hooft large N limit (N being the rank of

the Chern-Simons gauge group).

Perhaps the most physically intriguing property of these theories is

Bose-Fermi duality which states that Chern-Simons coupled bosonic and

fermionic matter theories are equivalent to each other. Another

(related) stark consequence of the Chern-Simons coupling is an

'exclusion principle' for the bosonic matter theory - analogous to the

Pauli exclusion principle - that was observed in the occupation number

distribution. Though the observation was initially made in the large N

limit of these theories, we offer a deeper structural explanation that

holds for all finite values of N albeit in a convenient

non-relativistic limit of the theories.

Done