A test of bosonization at the level of four-point functions in Chern-Simons vector models

• Published in: The journal of high energy physics Vol. 2015; no. 12; pp. 1 - 20
• Main Authors: Bedhotiya, Akshay, Prakash, Shiroman
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Coupling; Elementary Particles; Fermions; High energy physics; Joining; Mathematical analysis; Mathematical models; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; String Theory; Symmetry; Vectors (mathematics); Duality in Gauge Field Theories; Chern-Simons Theories; 1/N Expansion; Higher Spin Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP12(2015)032

A bstract We study four-point functions in Chern-Simons vector models in the large N limit. We compute the four-point function of the scalar primary to all orders in the ‘t Hooft coupling λ = N/k in U ( N ) k Chern-Simons theory coupled to a fundamental fermion, in both the critical and non-critical theory, for a particular case of the external momenta. These theories cover the entire 3-parameter “quasi-boson” and 2-parameter “quasi-fermion” families of 3-dimensional quantum field theories with a slightly-broken higher spin symmetry. Our results are consistent with the celebrated bosonization duality, as we explicitly verify by calculating four-point functions in the free critical and non-critical bosonic theories.