PIRSA:13030106

Large N Chern-Simons-matter theories and three dimensional bosonization

APA

Aharony, O. (2013). Large N Chern-Simons-matter theories and three dimensional bosonization. Perimeter Institute. https://pirsa.org/13030106

MLA

Aharony, Ofer. Large N Chern-Simons-matter theories and three dimensional bosonization. Perimeter Institute, Mar. 12, 2013, https://pirsa.org/13030106

BibTex

          @misc{ pirsa_13030106,
            doi = {},
            url = {https://pirsa.org/13030106},
            author = {Aharony, Ofer},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Large N Chern-Simons-matter theories and three dimensional bosonization},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {mar},
            note = {PIRSA:13030106 see, \url{https://pirsa.org}}
          }
          

Abstract

I will discuss the conformal theories of N complex scalars or fermions in 2+1 dimensions, coupled to a U(N) Chern-Simons (CS) theory at level k. In the large N limit these theories have a high-spin symmetry, and, as I will review, they are dual to Vasiliev's high-spin gravity theories on four dimensional anti-de Sitter space. Maldacena and Zhiboedov showed that the high-spin symmetry determines the 2-point and 3-point functions of these theories at large N, up to two parameters. The duality to Vasiliev's gravity suggests that there is some mapping between the CS+scalar and CS+fermion theories (when one adds a quartic coupling to the scalar theories, to flow to their "critical fixed point"). We compute explicitly the large N limit of some 2-point and 3-point functions in these theories. We show that the results match with the general results of Maldacena and Zhiboedov, and they are consistent with an equivalence between the critical theory of N scalars coupled to a U(N) CS theory at level k, and the theory of k fermions coupled to a U(k) CS theory at level (N-1/2). We conjecture that this large N equivalence may be an exact duality between the scalar and fermion theories also at finite N, thus providing a bosonization of the fermionic theory. Similar results hold for real scalars (fermions) when U(N) is replaced by O(N).