Work

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

Year: 2020

Type: article

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 $$ \mathcal{N} $$ 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 $$ {J}_0^f=\overline{\psi}\psi $$ J 0 f = ψ ¯ ψ and $$ {J}_0^b=\overline{\phi}\phi . $$ J 0 b = ϕ ¯ ϕ . Interestingly, because $$ \left\langle {J}_0^f{J}_0^f{J}_0^b\right\rangle $$ J 0 f J 0 f J 0 b 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.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep04(2020)207

Authors: Karthik Inbasekar, Sachin Jain, Vinay Malvimat, Abhishek Mehta, Pranjal Nayak, Tarun Sharma