Bootstrap experiments on higher dimensional CFTs

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 $N<N_{\ast }$, where $N_{\ast }\sim 15$ in $d=4$ and $N_{\ast }\sim 20$ in $d=5$.

22 pages, 20 figures

References in corpus (13)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• Bounds in 4D Conformal Field Theories with Global Symmetry
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Bounds on OPE Coefficients in 4D Conformal Field Theories
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap

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