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2017

Bootstrap experiments on higher dimensional CFTs

Nakayama, Yu

Understand

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 $d=5$.