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Abstract
Table of Integrals 40 1 Introduction
Summary of the Results
Conclusions
References

Constraints on parity violating conformal field theories in d = 3

Profile image of Subham Dutta ChowdhurySubham Dutta Chowdhury

Abstract

We derive constraints on three-point functions involving the stress ten-sor, 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 Mal-dacena. 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 (a 2 , 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.

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