Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions
By O. Aharony, Guy Gur-Ari, Ran Yacoby. 2012
295 citations recorded by the source corpus.
A bstractWe 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 Nf flavors) a $ \mathrm{U}{(k)_{{{{{N-{N_f}}} \left/ {2} \right.}}}} $ theory. Similar results hold for real scalars (fermions) coupled to the O(N)k Chern-Simons theory.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/65b129631f43b08413cc55c817d789e11aa3ac1a
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In Nuclear and High Energy Physics
Citations in the corpus
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- Correlators of large N fermionic Chern-Simons vector models (2012, methodology): “As in the bosonic theory [4], we can use these results to determine the parameters Ñ and λ̃ of Maldacena and Zhiboedov [3](9).”
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