Physics Seminar
Date: Monday, 28 October 2024
Time: 12:00 PM
Venue: Lecture Hall 1
Bose-Fermi duality in three dimensions and anyonic statistics
Naveen Prabhakar
ICTS.
28-10-24

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Abstract

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 in 2+1 dimensions to non-abelian Chern-Simons gauge theories, and explicit exact results for the partition functions in the 't Hooft large N limit (N being the rank of the Chern-Simons gauge group).

An analysis of these large N partition functions reveals anyonic physics in many aspects. The originally bosonic or fermionic fundamental particles now obey a modified occupation number distribution due to the coupling to Chern-Simons gauge fields, which, for instance, predicts an exclusion principle for the bosons. The large N partition functions also exhibit Bose-Fermi duality: the Chern-Simons coupled bosonic and fermionic matter theories are equal to each other under a particular map of the coupling constants of the two theories. Though these observations were initially made in the large N limit, these properties have a deeper structural explanation that holds for all finite values of N which can be seen in an appropriate non-relativistic limit.