Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap

Abstract

We investigate the conformal bootstrap approach to $O(N)$ symmetric CFTs in five dimension with particular emphasis on the lower bound on the current central charge. The bound has a local minimum for all $N>1$, and in the large $N$ limit we propose that the minimum is saturated by the critical $O(N)$ vector model at the UV fixed point, the existence of which has been recently argued by Fei, Giombi, and Klebanov. The location of the minimum is generically different from the minimum of the lower bound of the energy-momentum tensor central charge when it exists for smaller $N$. To better understand the situation, we examine the lower bounds of the current central charge of $O(N)$ symmetric CFTs in three dimension to compare. We find the similar agreement in the large $N$ limit but the discrepancy for smaller $N$ with the other sectors of the conformal bootstrap.

5 pages, 6 figures. v2: minor changes

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• Critical exponents of O(N) models in fractional dimensions
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• A Semidefinite Program Solver for the Conformal Bootstrap
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Inverse Bootstrapping Conformal Field Theories
• New method for the conformal bootstrap with OPE truncations
• The Epsilon-Expansion from Conformal Field Theory
• Six dimensional Landau-Ginzburg-Wilson theory
• Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap
• autoboot: A generator of bootstrap equations with global symmetry