# Bootstrap experiments on higher dimensional CFTs

## TL;DR

This paper identifies non-trivial kinks in the unitarity bounds of scalar operators in higher-dimensional SU(N) symmetric conformal field theories, revealing a conformal window and dimension-dependent features.

## Contribution

It reports the existence of kinks in the unitarity bounds for scalar operators in higher-dimensional CFTs with SU(N) symmetry, highlighting a conformal window and dimension-specific properties.

## Key findings

- Kinks exist in dimensions less than 6.
- Kinks occur when unitarity bounds equal space-time dimension.
- A conformal window exists for N less than approximately 15 in 4D and 20 in 5D.

## Abstract

Recent programs on conformal bootstrap suggest an empirical relationship between the existence of non-trivial conformal field theories and non-trivial features such as a kink in the unitarity bound of conformal dimensions in the conformal bootstrap equations. We report the existene of non-trivial kinks in the unitarity bound of scalar operators in the adjoint representation of the $SU(N)$ symmetric conformal field theories. They have interesting properties (1) the kinks exist in $d<6$ dimensions (2) the location of kinks are when the unitarity bound hits the space-time dimension $d$ (3) there exists a "conformal window" of $N<N_*$, where $N_* \sim 15 $ in $d=4$ and $N_* \sim 20$ in $d=5$.