Mellin space bootstrap for global symmetry

TL;DR

This paper uses Mellin space techniques to analytically bootstrap conformal field theories with $O(N)$ symmetry, computing operator dimensions and OPE coefficients up to third order in epsilon expansion, and exploring large $N$ limits.

Contribution

It introduces a Mellin space bootstrap approach for $O(N)$ symmetric CFTs, deriving new higher-order epsilon expansion results and analyzing large $N$ behavior.

Findings

Computed anomalous dimensions and OPE coefficients up to $O()$ in epsilon expansion.

Reproduced known results and derived new results for $O(N)$ models.

Analyzed large $N$ limit, confirming known leading order results.

Abstract

We apply analytic conformal bootstrap ideas in Mellin space to conformal field theories with $O(N)$ symmetry and cubic anisotropy. We write down the conditions arising from the consistency between the operator product expansion and crossing symmetry in Mellin space. We solve the constraint equations to compute the anomalous dimension and the OPE coefficients of all operators quadratic in the fields in the epsilon expansion. We reproduce known results and derive new results up to $O(\epsilon^3)$. For the $O(N)$ case, we also study the large $N$ limit in general dimensions and reproduce known results at the leading order in $1/N$.