Conformal field theories in fractional dimensions

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...

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Bibliographic Details
Published in:Physical review letters 2014-04, Vol.112 (14), p.141601-141601, Article 141601
Main Authors: El-Showk, Sheer, Paulos, Miguel, Poland, David, Rychkov, Slava, Simmons-Duffin, David, Vichi, Alessandro
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.112.141601