Mellin space bootstrap for global symmetry

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 $1/N$.

typos corrected

References in corpus (11)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Writing CFT correlation functions as AdS scattering amplitudes
• Bounds on 4D Conformal and Superconformal Field Theories
• Spinning AdS Propagators
• Mellin amplitudes for $Ad{S}_5\times S^5$
• A Mellin space approach to the conformal bootstrap
• Conformal Bootstrap in Mellin Space
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Generalized Wilson-Fisher critical points from the conformal OPE
• Critical capacitance and charge-vortex duality near the superfluid to insulator transition

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