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Critical O(N) models in 6ε dimensions

Lin Fei, Simone Giombi, and Igor R. Klebanov
Phys. Rev. D 90, 025018 – Published 14 July 2014

Abstract

We revisit the classic O(N) symmetric scalar field theories in d dimensions with interaction (ϕiϕi)2. For 2<d<4 these theories flow to the Wilson-Fisher fixed points for any N. A standard large N Hubbard-Stratonovich approach also indicates that, for 4<d<6, these theories possess unitary UV fixed points. We propose their alternate description in terms of a theory of N+1 massless scalars with the cubic interactions σϕiϕi and σ3. Our one-loop calculation in 6ε dimensions shows that this theory has an IR stable fixed point at real values of the coupling constants for N>1038. We show that the 1/N expansions of various operator scaling dimensions match the known results for the critical O(N) theory continued to d=6ε. These results suggest that, for sufficiently large N, there are 5-dimensional unitary O(N) symmetric interacting conformal field theories (CFTs); they should be dual to the Vasiliev higher-spin theory in AdS6 with alternate boundary conditions for the bulk scalar. Using these CFTs we provide a new test of the 5-dimensional F theorem, and also find a new counterexample for the CT theorem.

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  • Received 20 May 2014

DOI:https://doi.org/10.1103/PhysRevD.90.025018

© 2014 American Physical Society

Authors & Affiliations

Lin Fei1, Simone Giombi1, and Igor R. Klebanov1,2

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 2Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA

See Also

Three loop analysis of the critical O(N) models in 6ε dimensions

Lin Fei, Simone Giombi, Igor R. Klebanov, and Grigory Tarnopolsky
Phys. Rev. D 91, 045011 (2015)

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Vol. 90, Iss. 2 — 15 July 2014

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