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Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions
Ist Teil von
The journal of high energy physics, 2012-12, Vol.2012 (12), Article 28
Ort / Verlag
Berlin/Heidelberg: Springer-Verlag
Erscheinungsjahr
2012
Link zum Volltext
Quelle
Springer for R&D Journals
Beschreibungen/Notizen
A
bstract
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 λ ≡
N
/
k
. We compute some correlation functions in this theory exactly as a function of λ, 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
theory. Similar results hold for real scalars (fermions) coupled to the
O
(
N
)
k
Chern-Simons theory.