Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions

TL;DR

This paper computes correlation functions in a large N Chern-Simons-matter theory, demonstrating a precise bosonization duality between scalar and fermionic theories in three dimensions, consistent with high-spin symmetry predictions.

Contribution

It provides an exact large N calculation of correlators in Chern-Simons-matter theories and establishes a detailed bosonization duality in three dimensions.

Findings

Correlation functions match high-spin symmetry predictions.

Exact duality between scalar and fermionic Chern-Simons theories at large N.

Potential extension of duality to finite N and k values.

Abstract

We consider the conformal field theory of N complex massless scalars in 2+1 dimensions, coupled to a U(N) Chern-Simons theory at level k. This theory has a 't Hooft large N limit, keeping fixed \lambda = N/k. We compute some correlation functions in this theory exactly as a function of \lambda, in the large N (planar) limit. We show that the results match with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have high-spin symmetries in the large N limit. It has been suggested in the past that this theory is dual (in the large N limit) to the Legendre transform of the theory of fermions coupled to a Chern-Simons gauge field, and our results allow us to find the precise mapping between the two theories. We find that in the large N limit the theory of N scalars coupled to a U(N)_k Chern-Simons theory is equivalent to the Legendre transform of the theory of k fermions coupled to a U(k)_N Chern-Simons theory, thus providing a bosonization of the latter theory. We conjecture that perhaps this duality is valid also for finite values of N and k, where on the fermionic side we should now have (for N_f flavors) a U(k)_{N-N_f/2} theory. Similar results hold for real scalars (fermions) coupled to the O(N)_k Chern-Simons theory.