# Bootstrap and collider physics of parity violating conformal field theories in $d=3$

## TL;DR

This paper investigates parity violating effects in three-dimensional conformal field theories, revealing new operator structures, analyzing their implications for crossing symmetry, and deriving collider bounds specific to parity odd interactions.

## Contribution

It introduces a new tower of double trace operators in the t-channel for parity violating theories and analyzes their impact on crossing equations and collider bounds.

## Key findings

- Parity odd s-channel stress tensor blocks lack logarithmic singularities.
- A new tower of double trace operators is necessary for crossing symmetry.
- Parity violating terms lead to a square root branch cut in collider bounds.

## Abstract

We study the crossing equations in $d=3$ for the four point function of two $U(1)$ currents and two scalars including the presence of a parity violating term for the $s$-channel stress tensor exchange. We show the existence of a new tower of double trace operators in the $t$-channel whose presence is necessary for the crossing equation to be satisfied and determine the corresponding large spin parity violating OPE coefficients. Contrary to the parity even situation, we find that the parity odd $s$-channel light cone stress tensor block do not have logarithmic singularities. This implies that the parity odd term does not contribute to anomalous dimensions in the crossed channel at this order in light cone expansion. We then study the constraints imposed by reflection positivity and crossing symmetry on such a four point function. We reproduce the previously known parity odd collider bounds through this analysis. The contribution of the parity violating term in the collider bound results from a square root branch cut present in the light cone block as opposed to a logarithmic cut in the parity even case, together with the application of the Cauchy-Schwarz inequality.