Locate the crossing dimension and test exceptional-point behavior in the iφ^5 universality class

Determine the precise value of the spacetime dimension d* in the interval 2 < d* < 3 at which the scaling dimensions of the operators φ and φ^2 cross in the PT-symmetric quintic scalar field theory S = ∫ d^d x [ (1/2)(∂_μ φ)^2 + g φ^5/120 ] with g ∈ iℝ, and ascertain whether this crossing exhibits exceptional-point behavior characteristic of non-Hermitian systems.

Background

Using two-sided Padé resummations of the 10/3−ε expansion constrained by exact two-dimensional minimal model data, the authors find that the scaling dimensions of the PT-odd operator φ and the PT-even operator φ^2 approach and cross for some d in (2,3). Since the operators belong to different PT sectors, the authors anticipate no symmetry obstruction to a genuine crossing.

They highlight the need for a quantitative analysis to locate the crossing dimension d* and to test for possible exceptional-point behavior, which can occur in non-Hermitian systems with PT symmetry, but leave this investigation for future work.