Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory

Abstract

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 $$ \mathcal{N} $$ = 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 J 0 f = ψ ¯ ψ $$ {J}_0^f=\overline{\psi}\psi $$ and J 0 b = ϕ ¯ ϕ . $$ {J}_0^b=\overline{\phi}\phi . $$ Interestingly, because J 0 f J 0 f J 0 b $$ \left\langle {J}_0^f{J}_0^f{J}_0^b\right\rangle $$ is a contact term, the four point function of J 0 f $$ {J}_0^f $$ 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 J 0 b $$ {J}_0^b $$ four-point function receives an additional contribution compared to the free theory expression due to the J 0 f $$ {J}_0^f $$ exchange. We find that the double discontinuity of this single trace operator J 0 f $$ {J}_0^f $$ vanishes and hence it only contributes to AdS-contact term.

Keywords

• 1/N Expansion
• Chern-Simons Theories
• Higher Spin Symmetry
• Field Theories in Lower Dimensions