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 conformal field theories 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 ϕ4 theory in the ϵ expansion.
Highlights
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 conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D
It is natural to ask, does crossing symmetry have anything to say about the space of conformal field theories (CFTs) in noninteger dimensions? Can we find a family of solutions to the crossing symmetry constraint that interpolates between the 2D Ising model, the 3D Ising model, and the 4D free scalar? The purpose of this Letter is to start addressing these questions
Summary
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Sheer El-Showk,1,2 Miguel Paulos,3 David Poland,4 Slava Rychkov,2,5 David Simmons-Duffin,6 and Alessandro Vichi7 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 φ4 theory in the ε expansion.
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