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 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.
Institut de Physique Théorique CEA Saclay, CNRS-URA 2306, 91191 Gif sur Yvette, France and CERN, Theory Division, CH-1211 Geneva 23, Switzerland.
Sheer
S
El-Showk
Department of Physics, Brown University, Box 1843, Providence, Rhode Island 02912-1843, USA.
Miguel
M
Paulos
Department of Physics, Yale University, New Haven, Connecticut 06520, USA.
David
D
Poland
CERN, Theory Division, CH-1211 Geneva 23, Switzerland and Laboratoire de Physique Théorique, École Normale Supérieure, Paris France and Faculté de Physique, Université Pierre et Marie Curie, Paris, France.
Slava
S
Rychkov
School of Natural Sciences, Institute for Advanced Study, Princeon, New Jersey 08540, USA.
David
D
Simmons-Duffin
Theoretical Physics Group, Ernest Orlando Lawrence Berkeley National Laboratory and Center for Theoretical Physics, University of California, Berkeley, California 94720, USA.
Alessandro
A
Vichi