A bstract We present a novel semiclassical framework tailored to determine the scaling dimensions of heavy neutral composite operators in conformal field theories (CFTs) which are inaccessible with other current methodologies. It utilizes the state-operator correspondence to map the desired scaling dimensions to the semiclassical energy spectrum of periodic homogeneous field configurations on a cylinder. As concrete applications, we provide detailed analyses for the ϕ 4 theory near four dimensions and ϕ 6 near three dimensions, semiclassically determining the full spectrum of neutral operators transforming according to different Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.
Antipin et al. (Wed,) studied this question.