Conformal Field Theories in Fractional Dimensions

Abstract

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of phi^4 theory in the epsilon-expansion.

11 pages, 4 figures - references updated - one affiliation modified

References in corpus (7)

• Holography from Conformal Field Theory
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Bounds on 4D Conformal and Superconformal Field Theories
• The $(2,0)$ superconformal bootstrap
• Bootstrapping the 3d Ising twist defect
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Central Charge Bounds in 4D Conformal Field Theory

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