Wilson-Fisher fixed points for any dimension

Abstract

The critical behavior of a non-local scalar field theory is studied. This theory has a non-local quartic interaction term which involves a real power -βof the Laplacian. The parameter βcan be tuned so as to make that interaction marginal for any dimension. The lowest order Feynman diagrams corresponding to coupling constant renormalization, mass renormalization, and field renormalization are computed. In all cases a non-trivial IR fixed point is obtained. Remarkably, for dimensions different from 4, field renormalization is required at the one-loop level. For d=4, the theory reduces to the usual local ϕ^{4} field theory and field renormalization is required starting at the the two-loop level. The critical exponents νand ηare computed for dimensions 2,3,4 and 5. For dimensions greater than four, the critical exponent ηturns out to be negative for ε>0, which indicates a violation of the unitarity bounds.

12 pages, 5 figures

References in corpus (3)

• Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology
• Uncovering novel phase structures in ${\square }^k$ scalar theories with the renormalization group
• Critical behaviour of a non-local ϕ^{4} field theory and asymptotic freedom

Cited by in corpus (2)

• Symmetry breaking and RG flows with higher dimensional operators
• On RG flows in Generalized Effective Field Theory