Wilson-Fisher fixed points for any dimension

The critical behavior of a nonlocal scalar field theory is studied. This theory has a nonlocal quartic interaction term which involves a power −β of the Laplacian. The power −β is tuned so as to make that interaction marginal for any dimension. This leads to integer or half-integer values for β, dep...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. D 2019-12, Vol.100 (11), p.1, Article 116004
Main Author: Trinchero, R.
Format: Article
Language:English
Subjects:
Computation
Feynman diagrams
Field theory
Integers
Scalars
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The critical behavior of a nonlocal scalar field theory is studied. This theory has a nonlocal quartic interaction term which involves a power −β of the Laplacian. The power −β is tuned so as to make that interaction marginal for any dimension. This leads to integer or half-integer values for β, depending on the space dimension. Introducing an auxiliary field, it is shown that the theory can be renormalized by means of local counterterms in the fields. The lowest order Feynman diagrams corresponding to coupling constant renormalization, mass renormalization, and field renormalization are computed. In all cases, a nontrivial IR fixed point is obtained. Remarkably, for dimensions other than 4, field renormalization is required at the one-loop level. For d=4, the theory reduces to the usual local ϕ4 field theory, and field renormalization is required starting at the two-loop level. The critical exponents ν and η are computed for dimensions 2, 3, 4, and 5. For dimensions greater than 4, the critical exponent η turns out to be negative for ε>0, which indicates a violation of the unitarity bounds.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.100.116004