Correlation functions in N=2 Supersymmetric vector matter Chern-Simons theory

Abstract

Correlation functions of the higher-spin current operators in large N Chern-Simons theories are important to understand approximate higher-spin symmetries in these theories. Moreover, they also provide stronger checks for conjectured dualities in these theories. In this paper, we compute the two, three and four-point functions of the operators in the spin zero multiplet of N = 2 Supersymmetric vector matter Chern-Simons theory at large N to all orders of ’t Hooft coupling. While the two- and three-point functions are computed by solving the Schwinger-Dyson equation, this method becomes intractable for the computation of the four-point functions. Thereby, we use bootstrap method to evaluate four-point function of scalar operator Jf0=ψ¯¯¯ψ and Jb0=ϕ¯¯¯ϕ. Interestingly, because ⟨Jf0Jf0Jb0⟩ is a contact term, the four point function of Jf0 operator resembles the corresponding correlation function in the free theory, up to overall coupling constant dependent factors and up to some ‘bulk AdS’ contact terms. On the other hand the Jb0 four-point function receives an additional contribution compared to the free theory expression due to the Jf0 exchange. We find that the double discontinuity of this single trace operator Jf0 vanishes and hence it only contributes to AdS-contact term.