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.