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Constraints on parity violating conformal field theories in $d=3$ · Around

2017

Constraints on parity violating conformal field theories in $d=3$

Chowdhury, Subham Dutta, David, Justin R., Prakash, Shiroman

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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 $\langle T T T \rangle$ and $ \langle j j T \rangle$ correlation functions which are unique to three space-time dimensions.
Let the parameters which determine the $\langle T T T \rangle$ correlation function be $t_4$ and $\alpha_T$ , where $\alpha_T$ is the parity-violating contribution.
Similarly let the parameters which determine $ \langle j j T \rangle$ correlation function be $a_2$, and $\alpha_J$ , where $\alpha_J$ is the parity-violating contribution.

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