Constraints on parity violating conformal field theories in d = 3

Abstract

Abstract We derive constraints on three-point functions involving the stress tensor, T, and a conserved U(1) current, j, in 2+1 dimensional conformal field theories that violate parity, using conformal collider bounds introduced by Hofman and Maldacena. Conformal invariance allows parity-odd tensor-structures for the 〈T T T〉 and 〈jjT〉 correlation functions which are unique to three space-time dimensions. Let the parameters which determine the 〈T T T〉 correlation function be t 4 and α T , where α T is the parity-violating contribution. Similarly let the parameters which determine 〈jjT〉 correlation function be a 2, and α J , where α J is the parity-violating contribution. We show that the parameters (t 4, α T ) and (a2, α J ) are bounded to lie inside a disc at the origin of the t 4 - α T plane and the a 2 - α J plane respectively. We then show that large N Chern-Simons theories coupled to a fundamental fermion/boson lie on the circle which bounds these discs. The ‘t Hooft coupling determines the location of these theories on the boundary circles.

Keywords

• Conformal Field Theory
• Chern-Simons Theories
• 1/N Expansion
• Higher Spin Symmetry