arXiv subjects

Jacob Hafjall

Publications and source records attributed to Jacob Hafjall.

3 recordsLinked to original sources

arXiv2026

Renormalization and Non-perturbative Dynamics in Conformal Quantum Mechanics

We study conformal quantum mechanics by first considering the perturbative $S$-matrix in various dimensions. The model has two couplings and we study perturbatively the degree of ultraviolet divergences arising in the interplay between the two couplings. We then focus on the inverse square potential in one spatial dimension and compute the beta function to arbitrarily perturbative and non-perturbative orders. This we do in both the bound state sector and scattering sector. We provide explicit, exact and infinite series results of the first few non-perturbative orders.

quant-ph↗

arXiv2025

Semiclassical Canovaccio for Composite Operators

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 $\phi^4$ theory near four dimensions and $\phi^6$ near three dimensions, semiclassically determining the full spectrum of neutral operators in the traceless symmetric Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.

hep-th↗

arXiv2025

Exact Results for the Spectrum of the Ising Conformal Field Theory

We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising $\lambda\phi^4$ theory in $d=4-\epsilon$, we obtain the full spectrum of composite operators built out of $n$ fields transforming in the traceless-symmetric Lorentz representations to next-to-leading order in the double-scaling limit $n\rightarrow \infty$ and $\lambda \rightarrow 0$ with $\lambda n$ fixed. At any given order the semiclassical expansion resums an infinite number of Feynman diagrams. Combining our results with existing perturbative computations further yields the complete five-loop scaling dimensions in the $\epsilon$-expansion for the family of $\phi^n$ operators. Finally, in three dimensions the next-to-leading order semiclassical results supersede any other existing methodology for $n \gtrsim \mathcal{O}(10)$.

hep-th↗